Design and Construction of a CollaJ>sible Bicycle
Project #F95/S96-4 June 1996
Design Team Michael Gorban, Matt MeNulty, .Jason Bardo :MattBallas, Tom Rose, Dave Macioce
Advisor Professor George Adams Table of Contents
1, DESIGN OBJECTIVES AND CONCEPT DESIGN SELECTION
------·------1-6
COLLAPSIBLE BICYCLE DESIGN PROCEDURE 2-8 ______
3 FINAL CONCEPT DESIGN ______3-10
3.1 Concept Design GA-4 ...... 3-10
4, MAIN SUPPORT BAR ______4-13
4.1 Description ...... ,...... 4-13
4.2 Initial Design ...... 4-13
4.3 Redesign ...... 4-13
4.4 Economic Considerations...... 4-15
4.5 M.echanics...... 4-16
4.6 Strength...... 4-16
4. 7 Dimensional Control ...... '" ...... , ...... ,4-16
4.8 Manufacturing Progress of Main Support Bar ...... ,...... 4-16
5. FRONT FORKAND STEEPJNG ASSEl\1BLY ______5-17
5.1 Initial Design ...... ,...... ,.,.,...... 5-17
5.2 Re-Design ...... 5-18
5.3 Second Redesign ...... 5-20
5.4 Materials ...... 5-21
5.5 Manufacturability ...... 5-21
5.6 Ergonomics ...... 5-22
5. 7 Strength of the Design...... S-22
6. TIE BAR 6-23 ------
6.1 Initial Design ...... 6-23
Requirements
Current Progress on Bar 6.5
MAIN HING E ------7-28
7.1 Fall Quarter: ...... 7-29
7.2 Spring Quarter: ...... 7-29
7.3 Preliminary Hinge Designs Calculations (Fall Quarter) ...... 7-29
7.4 Final Hinge Design #1 ...... , ...... 7 -31
7.5 Dimensions of Final Hinge Design #1 ...... ,...... 7-33
7.6 Preliminary Stress Calculations (Fall Quarter) ...... 7-34
7.7 Preliminary Stress Calculations (Spring Quarter)...... ,...... 7-34
7.8 Proposed Modificationsto Strengthen the Joint...... , ...... 7-34
7.9 Potential Problems and Proposed Solutions ...... , ...... 7-35
7.10 Necessary Modifications to the Main Hinge Design (Spring Quarter) ...... 7-35
7.11 Design Change #1 and Proposed Modifications...... 7-35
7.12 Design Change #2 and Proposed Modifications...... 7-36
7.13 Optional Modifications to the Main Hinge Design (Spring Quarter) ...... 7-36
7.14 Optional Design Change #1 ...... ,...... 7-37
7.15 Optional Design Change #2...... ,...... 7-37
7.16 Final Hinge Design #2 (Spring Quarter) ...... 7-38
7.17 Materials ...... 7-38
7.18 Manufacturing Considerations...... 7-39
8. SEATPOST JOINTS AND ASS EMBL Y ______8-48
8.1 Initial Design ...... ,...... 8-48
8.2 Overall Strength of the Seatpost ...... ,...... 8-48
8.3 Allowable Space Requirement ...... 8-48
8.4 Adaptability ...... J�-49
8.5 Re-designing the Seatpost ...... 8-49
8.6 Support Beams...... S-50
8. 7 Seat Adjustment Member ...... 8-50
8.8 Seatpost Main Axle ...... 8-50
8.9 Support Plates ...... ,, .. ,,., .. S-51
8.10 Turnbuckle
�Ul The
2 8.12 Economic Considerations...... 8-52
8.13 Dimensional Control ...... 8-52
8.14 Mechanics/Strength: ...... 8-52
8.15 Overall Strength...... S-53
8.16 Seat Post Axle ...... 8-53
8.17 Support Beams...... S-53
5 9. OVERALL DESIGN CONSID ERATIONS ______9- 4
9.1 Drivetrain Design ...... 9-54
9.2 Triangular Frame Assembly
10. SUMMARY AND RECO MMEND ATIONS ______l0-61
11. REFERENCES ______11-62
3 of Figures
Figure final concept design initial design sketch 3-10 Figure 2- main support bar, final conceptual design 14 15 Figure 3 - main support bar with tie bar and fo rk Figure 4 - alternate view of main support bar, tie and fork 4-15 Figure 5 - fr ont fork 5-19 Figure 6 - handlebar 5-20 5-20 Figure 7 - complete fr ont assembly Figure 8 - tie bar 6-27 Figure 9 - alternate view of tie bar 6-27 7-28 Figure 10 - location of main hinge 1 11 - final hinge design Figure 12- exploded view ofhinge 7-42
13 - proposed modification of 7-43 - old and new hinge designs 7-44 7-45 Figure 15 - location of welding plate 7-46 Figure 16 - final end plug/central core design 7-47 Figure 17 - aluminum block 9-55 Figure 18 - sprocket diagram 9-59 Figure 19 - rear triangle
List of Tables
Table 1 -tube diameter dimensions 7-33 Table 2 - gear ratio selection 9-56 9-58 Table 3 - velocity considerations
4 Abstract
This report discusses the final conceptual design, engineering analysis and construction of a collapsible bicycle. The bicycle is designed such that it will easily achieve 8 MPH over normal city streets while carrying a rider of 250 pounds. collapsed size of the bicycle needs to be 6xl6x20 inches, which is roughly the size of a small suitcase. Urban commuters will be targeted as the users of this bicycle. We have achieved a final conceptual design which meets these guidelines and constructed a fully functional model the bicycle. The working model proves that our design functions properly and satisfiesthe given constraints, it also shows where improvements to the design would be necessary fo r a marketable product.
Acknowledgments
design group would like to thank Professor Adams and Professor Kowalski for their guidance throughout the life of this project. Also, without the help of Jonathan Doughty and Jim Surrette this project would never have been completed. Professor Messac was also instrumental to the success of this project with the high standards he set for us.
1-5 1. Design Objectives and Concept Design Selection Criteria
The objective of this project is to design and manufacture a collapsible bicycle. The overall dimensions of the bicycle when in its folded position will be 6 x 16 x 20 inches, this is similar to the dimensions of an average briefcase. Urban commuters will be the target market for the bicycle. Some requirements that are essential for a successful design are listed here:
1111 Able to reach a maximum stable speed of 8
1111 be assembled and disassembled with ease.
1111 Able to support a of 250 lbs on normal urban streets.
111 Can satisfy allbicycle safety codes.
• Has potential to be outfitted with an electric motor.
The weight of the prototype is not a design priority; however, it does need consideration so that the bicycle will be able to be assembled with a relative amount of ease. At this time the potential for outfitting the bike with an electric motor has not been investigated, it proved to be beyond the scope of our time constraints.
The selection process for proposed concept designs was developed by working the design requirements into more specific criteria to judge the possible selections. These criteria allowed for more detailed thought on each aspect of a design. An example of this breakdown is comparing the requirement that the bicycle should support a load of 250 pounds and considering the criteria of fr ame joint strength. The requirements provided a starting point, which prompted the realization that the forces the bicycle will be experience will not allow the use some types methods materials.
Another example is requirement ease travel over streets aspects
1-6 needs to be able to avoid hitting obstacles without worrying about rider stability or controL In this initial phase details were neglected and left to the individual design teams which will explained furtherin the following sections. 2. Collapsible Bicycle Design Procedure
In the design of a new product, such as a bicycle, many initial concept designs are needed order to all reasonable and ways achieving the design objectiveso Therefore, the design meetings consist mainly of brain- storming sessions in which all members of the groups present their ideas and thoughts freelyo
sessions are started with each group member developing at least two possible designso A group meeting is then held and each design is analyzed for feasability using following criteria:
Iii ease of assembly/disassembly
1111 fr ame/joint strength
1111 stability
11111 control
111 number of pieces
111 comfort/ergonomics
• availability of parts
1111 overall cost
Eventually the number of possible designs is narrowed down to four. These four designs are presented at the combined group meeting where everyone has opportunity to comment on each desigR After discussing the different concept designs, the group schedules another meeting at which the final concept design is decided upon. Once the final design is chosen, the next task is to break the concept bicycle into subsystems and to assign design teams to each subsystem.
Brain-storming sessions need to be conducted an open forum where every group member has an they
2-8 proceed. designs are given equal analysis and discussion time in order to best achieve the objectives.
2-9 3. Final Concept Design
As a result of the brainstorming sessions and group discussions a final design was chosen. detailed explanation of concept design can be found in Appendix of this report.
3.1 Concept Design GA-4 This design consists of approximately removable parts and a number of hinged components, all of which are based around the 12 inch rear wheel and triangle subframe assembly. Figure 1 provides a sketch of the initial design, which was referred to as
10.E'l:
--- - 3150: ------.1 4! )[)
Figure final concept design initial design sketch 1-
The removable parts will include the fr ont wheel, the hand-grip cross member on top of the handle bars, and the support member connecting the seat post to the
forward frame. The main section of this bicycle design is the rear wheel I triangle subframe assembly, to which all of hinged components, such as the seat post and fo nvard will be
3-10 fold this bike, follow these steps:
1. Remove the front wheel (using the quick release latch).
2. Remove the support member connecting the seat post to the forward fr ame.
3. Remove the hand grips from the handle bars.
4. Fold the handle bars backwards towards the seat post until it is almost
parallel to the forward frame "'·A,LUJ•u
5. Fold the forward frame (and handle bars) underneath bicycle until the two parallel bars which make up this forward frame section straddle rear wheeL
6. Slide the forward section through the collar (located at the hinge) in the direction of the foot pedals. It should slide approximately 7 inches before it cannot slide any
7. the seat up until the base of seat post frame is released from its supporting collars.
8. Fold seat post forward, by removing the support pins.
9. Secure the front wheel, support member, and hand grips to their associated locations on the collapsed bicycle.
3.1.1 Advantages
11111 Unique joint design allows easy, efficient folding
1111 Two or three pieces
1111 Ease of assembly, no more than five minutes
3.1.2 Disadvantages
1111 Custom designed joints
111 Length handlebanL
II Width
11 design was chosen for its unique joint design and efficient folding sliding aspect of the joints allows the use of longer tubing which will help maintain structural integrity.
Once in the proposed folded po:sn1on, the bicycle will be very compact and will take advantage of most the space available. The rear triangle will act as the design center point and all sub-sections will be designed off ofthe triangle. There is a considerable amount of freedom in the design that will allow it to be easily modified throughout the design process. final design was broken into sections which were assigned to sub-groups as mentioned earlier. will cover the main support bar, the front fork and steering assembly, the tie-bar, the main joint assembly, and the seatpost joints.
3- 12 4. Main support bar
4.1 Description main support bar spans fr om the bottom bracket to the front fork head tube. Due to the folding method of the bike, the main support bar must be able to straddle rear wheel of the bike.. At the lower end of the main support bar, where it joins the main is a cap which prevents the bar sliding out of the hinge and provides a contact point with rear front of the main support bar must incorporate the head tube in such a way it able to support the front assembly. Also, there must be attachment points that will allow bar to connect the seatpost and the main support bar.
4.2 Initial Design Initially, the main support bar was designed using L5 inch square tubing and a number of welded connections. The first design used two bars coming from the main hinge to form the opening. It was determined that this design would not work since the necessary clearance for the pedals could not be attained. By switching to only one bar at the main hinge, we were able to achieve the necessary clearance and still allow for the rear tire slot. The welded square tubing proved to be a very cumbersome design and required a great deal of precision welding.
4.3 Redesign The shape of the main support bar was kept, but 1.125 inch diameter round tubing was chosen instead. Square tubing was kept for the region that engages with the main joint to combat the twisting problems that would be experienced round tubing. The round design involves having the tubing custom formed into and oval shape. connectors will be brazed to the main support tubes to incorporate the tie steering tube to support oval involves running through vertex and
4-i will be reinforced two gusset plates, one on top one on the bottom. The main support bar is shown in figure 2 follows.
Figure - main support conceptual design 2
This design is much less cumbersome than the square design. is much less welding involved and the tubing diameter is smaller which provides for a much more efficient design.
4) The following illustrations (figures 3 and show how the main support bar fitstogether with the front fork, stem and tie bar.
4-14 Figure main support bar with tie bar and fork 3
Figure alternate view of main support bar, tie bar, and fork 4-
4.4 Economic Considerations The cost of custom bent tubing proved to be too expensive for the design prototype so an alternate design was chosen. For the working prototype of the
collapsible bicycle, the long spans of the main support bar are made from 1. 5" rectangular, steel tube. Machined aluminum blocks form the holder for the
head tube and connection bracket the main hinge. All connections are made with 5/16 - 18 socket head cap screws and the head is held place with a damping mechanism. are the same as proposed
4- 1 5 model was easily constructed in the Northeastern machine shop, exlcusively using materials on hand.
4.5 Mechanics The mam support bar a bending stress, as well as a torsional stress. Bending stresses will come from the reaction force on the front wheel from the ground. With a 250 pound rider, the distribution of forces would provide for approximately a 100 pound force directed axially along the head tube. Also, impact forces must be taken consideration due to rough road surfaces, a detailed analysis of the forces exp�,::rienced by bicycle frame is being performed by the other bicycle group and the results can be found the appendix of report.
It was determined that 1.125 inch outer diameter and 0.995 inch inner diameter tubing (16 gauge) was more than sufficient to withstand the bending and torsional stresses experienced by the bar in a worst case scenario. This was determined by using a standard minimization optimization technique. opimization report can be found in the appendix B of this report.
4. 7 Dimensional Control Controlling the dimensions in manufacturing the main support bar will be very important The main support bar interacts with many of the other components on the bike, including the bar, the main hinge, the front fork and the rear triangle. Tolerances must be held order for the bar to functionproperly.
_4.8 Manufacturing Progress of Main Support Bar The main support bar has been completed successfully.
4-16 5. Front fork and Steering Assembly
The items mentioned in the steering/ fork section are shown below:
1111 Initial Design
11111 Economic Considerations
1111 Lab Analysis
1111 Dimension Control
1111 Ergonomics
5.1 Initial Design maJor concerns of the initial design were as follows, order of m importance:
1111 Wheel size
111 Strength of the steering column
= Foldability
!!!! Fork size
Originally, a front wheel a inch diameter was to be used and width of wheel, measured from the outside of the hub was to be 5.5 inches. The hub will be a quick release to ease the assembly and disassembly of the The front wheel size is important to the entire bicycle because it alter the fork angle of the bike which turn changes the feel the rider will experience.
basic design of the fork was determined by the size of the wheel. length of steering column is 20 inches with a double bar stemming from the set to the handle bars. are two reasons for double bar. First, the
5-1 7 strength will be doubled by minimizing torsional and bending forces, and second, when the bicycle is collapsed down the handle bars will straddle the rear wheel, just as the main frame will. The front wheel will have a quick release hub so that the front wheel will be removed easily and placed in the collapsed form. The handle bars will fold in towards the frame on both sides, by means of a quick release. This will give the handle bars a 6 inch width dimension. The stem has two clamps that close down onto a circular cross sectional bar, with grooves for better gnp.
The two major constraints for this project are strength and size. The foldability parameter is a difficult satisfY, because the bicycle will function even though the parameter is not met. The dimensional considerations makes this design interesting.
The basic design of the fork is determined by the size of the wheel. A standard fork will be used to minimize cost and ensure strength.
5.2 Re-Design The concerns of the redesign are slightly different than the initial design. The fork design has been altered to give a better response and overall handling of
the bicycle. The fr ont wheel size is now 10 inches in diameter. The fork still is straight, however a plate with a cutaway for the hub to go is attached to the front side of the fork The illustration of the plate attached to the fork is shown below in figure 5
5-18 Figure -front fork 5
The handling of the bicycle is better due to the fact that the center of gravity will be lower when the wheel is straight.
The stem was evaluated more closely to meet the strength requirements. The stem will has a quick release that closes down onto a round cross sectional bar with a pin for extra support. The reason for the change in cross section is because a large force pulling the steering column backwards could cause some slippage at the stem. By having the pin, there will be more a stable and secure hold onto the bar. The handlebar and complete assembly are shown in the following figures.
5-1 9 f)
Figure handlebar 6 -
Figure complete front assembly 7-
5.3 Second Redesign The concerns of the redesign for the spnng quarter are similar to the concerns from the Fall quarter. The front wheel diameter was changed from 10 inches to 8 inches so that collapsed dimensions are as small as possible and that the wheel can fit in to the commuter box (20" x 16" x 6'"'). The fork length is also to be shortened for following reasons. First, the ease of foldability and collapsed dimensions will be met and second, the ergonomics of the ride will be more suitable for the rider. An 8 inch diameter wheel will lower the center of
5-20 gravity even more than the 1 0 diameter wheel when in the straight position.
Rather than redesign an entire new head-set and stem, a standard ones have been purchased which will easily meet strength requirements and will be less expensive than a custom made prototype. The cross section of the handlebar that is clamped by the headset has been changed a to a round cross section. Some concerns have evolved regarding to the handle bars sliding with the change to a round cross section. problem has been alleviated by pinning the connection the stem and handlebars. The pin is removeable and can be inserted two positions, one for the assembled state and one for the collapsed state.
The cross section of the remaining bars of handle bar was changed from square to so that they could be made from commercially available pipe. The hinge that was designed the grips the handle bar has been changed and now consists of a coupling that connects pieces of pipe, when the coupling is unscrewed, the grip sections of the pipe are free to fold in. An elastic shock cord runs internallythrough the handlebars to hold the entire assemble together when the collapsed position.
5.4 1\-Iaterials The materials for the project have been determined by availability. The handlebars will be iron pipes, which are relatively easy to weld and are easily accessible at any hardware store. The headset will be cro-moly and can bought at any bicycle store. fork and front wheel are going to and have been obtained from an old bicycle.
5.5 Manufactu:rabiiity The only obstacle in this portion bicycle is welding. The handlebar requires welding of different areas. m was no machining Welding was s machine 5.6 Ergonomics ergonomics of the rider have been looked at more closely during the spring quarteL The results determined that fork angle will be 68 degrees from the ground to get the proper response that the rider will need for turning. This was determined by our co-workers on the bicycle project.
5.7 Strength of the Design The strength of the design at preliminary stages was evaluated by the stand point of joining points and pins. The main concerns are shear and torsional forces which be produced when turning or leaning from one side
5-22 6. Tie bar
6.1 Initial Design In the initial design of the collapsible bicycle, the tie bar was not detailed, in other words, it was just drawn in as a line; however, a need for the bar was seen because ofthe bicycle's folding mechanism. Something was needed to support the front member (connecting the main frame to the headset) while in the unfolded, riding position, as well as hold the seat post arrangement down while the bicycle was m use.
6.2 Requirements To start the design process a list of requirements the tie bar had to meet were drawn up. These features were as follows:
11 Be easily attached and unattached.
• Perform as a rigid, structural fr ame member m both tension and compressiOn.
Be made from common materials for ease of manufacturing and 11 assembly.
11 Have a semi-constant length in order to avoid designating a top and bottom section of the bar.
11 Be able to adapt to thr�ad wear, stretching, and loosening of the bicycle frame.
11 Be installed and removed without the use of tools.
Three ideas were presented as possible solutions to this design problem. They are as follows:
6-23 6.2.1 Option 1 The first idea for the tie bar was a cord connecting the seat post to the forward member. This idea would be easily attached/unattached, made, and assembled. A cord could be bought that would hold the bicycle together under a tensile load. However, it would fail under a compressive load such as the bicycle going over a pot-hole and experiencing a jarring motion.
6.2.2 Option 2 Another idea was to have the bar connect to the frame at either end and be a telescoping tube in the center section. The telescoping section would be pinned at regular intervals along its adjustment section to make it adaptable to any length change it may need. This design could be made to be easily attached/unattached, assembled, and perform well in both tension and compression. However, its major drawback is that as the bicycle goes through a break-in period, where the parts wear and loosen or a part gets bent and the length where the bar fits changes, it is hard to have a perfect fit for this tie bar. A situation that could arise would be that the rider would have to suffer through an uncomfortable ride because of the sloppy frame support. Another disadvantage of this design is that in order to make the bar adjustable holes would have to be drilled along its length, thereby making the tubes weaker.
6.2.3 Option 3 The final idea is similar to the previous except it uses threaded rod as the adjustment mechanism rather than pinned, telescoping tubes. This design would work as a turnbuckle, where both ends are held to the seat post and the front member, and each end has threaded rod coming from it. On one end the threaded rod is of the normal right-handed arrangement while on the other end the threaded rod has a left-handed thread. The threaded rods are connected with a tube with the proper female threads tapped into the ends, a turnbuckle. The threaded rods need to be opposite threads to produce a tightening effect. This design
6-24 encompasses all of the necessary features needed for the tie bar, especially the fine adjustment provided by the threaded rods.
The only further necessity is a locking mechanism for the turnbuckle. This would be done by having another nut on one of the threaded rods that would be tightened against the turnbuckle to hold it in place. The turnbuckle and the nut would both be made such that they would be easily tightened and loosened by hand.
Although the bar will mainly see tensile loads, the end connections need to be designed to hold the bar in place under both tensile and compressive forces. The ends consist of two hooks connected to the front member and the seat post. These hooks accept the 'T'- shaped ends of the tie bar. The advantage to having hook type end connections is that it is easier to remove the tie bar for folding the bicycle than of the other ideas considered. The hooks will have as low of a height as possible in order to not catch on any clothing. 3/8" diameter threaded rod is used to make the "T" connections so that they will be able to withstand the forces they will experience. The tie bar is shown in figures 8 and 9.
6.3 Current Progress on the Tie Bar
6. 3 . 1 Configuration Due to time and economic constraints the turnbuckle section of the tie bar
will be a 1;2 inch standard turnbuckle. This will take the place of the center section being a 1-1 1;2 inch diameter tube with the proper left and right hand threaded ends. See figure 8. Although the original design would have been sturdier, because the length of the center tube would be longer than a standard turnbuckle (thereby giving more support to the threaded rods), we believe that a standard arrangement will provide an adequate substitute for the prototype bicycle. The 'T' -ends and the hooks of the tie bar will keep their original arrangement
6-25 ll
tie bar 8
Figure - alternate view bar 9
6.5 Economic Considerations For the tie bar part of the bicycle, the major economic considerations are for ease of manufacturability. This encompasses making parts that require little or no machining, parts being readily available with no lead time or custom ordering, and assembly being done with standard methods that can be done in-house.
Because of the simplicity of this design we believe that there will be little economic impact with this part as compared to the rest of the bicycle. All parts for the tie bar are normal stock items at most distributors of these materials. only machining needed will hooks, which can Northeastern's not special
6-27 7. Main Hinge
Of all of the components which makeup the collapsible bicycle, one of the most important is the main hinge, located just forward of the rear wheel. The purpose of the hinge is to secure the fo rward frame member to the rear triangle assembly while the bicycle is being ridden, as well as to allow the fo r.vard frame to
be fo lded underneath the bicycle and slid fo rward when it is not in use. Figure 10 shows the location of the main hinge in relation to the other bicycle components.
Figure Location of Main Hinge 10-
Since the hinge is responsible fo r holding the fo rward frame member in place while the bicycle is being ridden, the final design will have to be able to withstand forces of large magnitudes. When the design group began discussing preliminary concepts fo r the hinge, its ability to handle these large forces was the one of the primary concerns. In addition, the size of the hinge and its ability to
7-28 explained in detail, from the initial conceptualization stages to the final design which was completed at the end of the FaH Quarter.
7 . 3 1 Initial Force Calculations at the Hinge Before discussing concepts and ideas regarding the main hinge design, the sub-group in charge of this component decided it would be more beneficial to first determine the forces that will be imposed on the hinge while it is in use. A number initial facts were known at this time which helped the sub-group in determining the forces. They were as follows:
• The maximum allowable rider weight (250 lbs).
• The rough dimensions of the bicycle frame.
• The general location of the main hinge.
Using these facts, the sub-group calculated the force imposed on the main hinge when a rider weighing 250 lbs. sits on the bicycle. In order to simplify the calculations, the effects of the cross member connecting the seat post to the forward frame member were neglected. Although the cross member would greatly reduce the forces acting on the main hinge, by neglecting its effects the group not only simplified the calculations, but was able to impose a factor of safety as welL
Appendix C shows the calculations used to determine the force imposed on the hinge by a 250 lb. rider. The resulting tensile force was found to be approximately 392.61 lbs.
7.3.2 PreliminaryHinge Designs Following the completion of the initial force calculations, the sub-group began formulating general concepts for the hinge design. Some of the more important considerations discussed included the following:
• The hinge assembly must be able to withstand the static forces calculated in the previous sectiono
7-30 • The hinge assembly must be able to withstand the momentary impact forces associated vvith hitting a bump in the road or riding offa curb.
• The hinge assembly must be able to withstand the torsional forces at the front collar.
• The hinge itself must be able to withstand the torsional forces.
• The collar which secures the forward frame member to the hinge itself must be designed such that it holds the forward frame member as tightly as possible while still allowing it to slide through when the bicycle is folded.
• The hinge must be able to rotate at least 180 degrees in order to allow the front section of the bicycle to fold into the proper position.
• The hinge can be no more than 3- 1/2 inches wide or else it will interfere with the locations of other bicycle components.
In considering these specifications, the design group discussed a number of designs. The most popular concepts discussed at this time were all based on a typical door hinge design. In the case of a standard door hinge, a number of collars, which are alternately secured to the door and the door frame, are all allowed to rotate around a central, load bearing core. When the idea of using this concept was proposed, the members of the group began to explore the associated advantages and potential problems which the design involved.
7.4 Final Hinge Design #1 The advantages of using a main hinge design based on a door hinge were found to far outweigh those of the other designs. After considering a number of different versions of this concept, a final design was eventually chosen. This hinge design was fo und to have many features and advantages that the others did not, including:
7-31 �& It allows for the easy removal the forward section (forward frame member, handle bars, fork, and front wheel) the bicycle.
• The hinge can be easily fabricated from standard steel p1pe stock (square and round).
• The preliminary stress calculations for the hinge components show that the hinge will be able to withstand the forces imposed on it.
The final hinge design, an exploded diagram of which is shown in figure 12, consists ofthe following components:
1 One forward collar assembly consisting of 3 separate collars and 2 braces" A square collar, used to hold the forward frame member, will be secured to the 2 rotating round collars via the 2 braces.
20 Three independent collar and bracket assemblies which will be welded to the rear triangle frame section of the bicycle.
3. One central core around which 2 round collars from component and the 3 collar/bracket assemblies (#2) will be free to rotate.
4. One Teflon sleeve which will surround the central core and allow the collars to rotate more freely.
5. Two end plugs used to secure the collars and central core in place. The end plugs each will consist of a round steel tube capable of snugly fitting inside the central core and a plate welded to the end of the tube. The end plate will have a diameter larger than the collars and will therefore be able to keep the core aligned inside the five collars.
6. One which will pass through a hole in one of the end plug end plates, through the central core, and through a hole in the second end plug end
7-32 plate. The bolt will be held in place with a wing nut and washer, and will in turn secure the end plugs and, accordingly, the entire main hinge assembl:y.
7.5 Dimensions of Final Hinge Design #1 Using a list of standard steel tubes, both round and square, the design group was to find tubes with dimensions appropriate fo r use in the hinge. During the time spent sizing hinge components, one of the major concerns came up was the need to find tubes with matching inside and outside diameters fo r collars, core, and the end plugs. This matching of inside and outside diameters will help the group constructing a hinge that have no undesirable play between the components.
Although many of the dimensions have been determined at this time, the dimensions of the brackets and the end plug and plates have yet to be finalized. Since there is no weight restriction on the bicycle, many of tubes were chosen fo r their large wall thicknesses, resulting in a much stronger hinge.. table below shows the tube diameter dimensions that have already been determined:
Table -Tube Diameter Dimensions
Round Collars (5) Outside Diameter 2.000 in. I Inside Diameter 1.625 in. Central Core (1) Outside Diameter 1.500 in.
inside Diameter 1.232 in. I End Plugs Outside Diameter 1.1875 in. I
I Inside Diameter 0.947 in.
Square Collar (1) Outside 1.750 in. I I Height/Width iI I Inside 1.510in.
7-3 3 7.6 PreliminaryStress Calculations (Fall Quarter) At this time, only preliminary stress calculations have been performed. The design group fo cused on the shear stresses imposed on the central core (both with and without the end plugs considered as load bearing components) and the maximum force, F, which the hinge will be able to withstand. Appendix C shows these calculations in detail.
When considering the end plugs as load bearing components, the maximum allowable force, F, was found to be approximately 117, 360 lbs., well above the static fo rce of 392.6llbs. calculated earlier. Without considering the end plugs as load bearing components, the maximum allowable fo rce, F, was found to be approximately 69, 006 lbs., still well above the static fo rce.
7.7 Preliminary Stress Calculations (Spring Quarter) At the beginning of the Spring Quarter, additional stress calculations were performed. This time through, the design sub-group fo cused on tensile failure in the three round collars. Again, no problems were found with the resulting maximum loads since they were all well above the static force of 392.61 lbs .. When the calculations were performed fo r the middle collar, the maximum load was found to be 27,000 lbs. For a single outer collar, the maximum load was found to be 10,800 lbs., and given that there are two of these collars working together, the maximum load can be considered as being 21 ,600 lbs ..
7.8 Proposed Modifications to Strengthen the Joint During the design process, a suggestion was made regarding a way to help to strengthen the main hinge against torsional loads. The suggestion involved extending the 2 square collar brackets past the collar itself and back around the rear frame of the bicycle as shown in figure 13. By extending these brackets, a portion of the torsional load which would have been imposed entirely on the hinge, is transferred to the rear frame.
7-34 7.9 Potential Problems and Proposed Solutions One potential problem which was brought up by Professor Kowalski during the large design group meeting involves dirt getting into the hinge and causing it to or other permanent damageo design sub-group charge of the hinge design has not looked depth a solution, they are considering installing a cover for the hinge which may help to solve problem. The group will investigate this and other solutions in the future.
7.10 NecessaryModifications to the Main Hinge Design (Spring Quarter} the beginning of the Spring Quarter, the main hinge sub-group was notified of two important changes made to overall bicycle design. These changes were fo und to have a direct impact on the hinge specifications and had to be addressed in form of modifications to the final design.
7.11 Design Change #1 and Proposed Modifications The first overall design change involves the width at the location where the hinge is to be secured to the rear triangleo Because the both the forward sprocket and pedals are located directly above the main hinge, they play an important role in determining the hinges overall dimensionso Originally, the location and dimensions ofthe sprocket and pedals allowed a maximum hinge width of3. inches with the final Fall Quarter design being approximately 32 5 inches wideo As a result of the frame modifications, the new maximum hinge width was determined to be inches.
The almost 18% reduction in the allowable hinge width initially posed a serious problem since it would require the elimination of the two outer collar/bracket assemblies. These assemblies made up two of the three connections between the main hinge and the rear triangleo By eliminating the two assemblies, the strength of the hinge/rear triangle connection would be reduced immensely.
Since the main hinge sub-group determined it would be necessary to two outer collar/bracket assemblies to meet new hinge
7-35 width limit, something needed to be done to strengthen the last remammg collar/bracket assembly. It was decided that instead of welding one bracket to the collar, two brackets would be used, thereby significantly increasing the strength of the connection. Figure 14 shows both the old and the modifiedhinge designs.
7.12 Design Change #2 and Proposed Modifications The second design change involved the location where the brackets would be welded to the rear triangle. The final design of the rear triangle indicated that the bearing case for the pedals will be located directly above the location of the main hinge. The sub-group responsible for the design of the rear triangle showed concern about the effects of welding the hinge brackets directly to the bearing housing. The sub-group wanted to keep the number of welds at the bearing housing to a minimum, thereby reducing the likelihood of heat related damage to the component. Since this component of the bicycle already had two structural components welded to it, they suggested installing a plate just behind the bearing casing where the welds could be made. This proposal was found adequate by the
main hinge sub-group and is shown in figure 15. This design requires that brackets be extended backwards so that they can be welded to the plate while still allowing the brackets to butt up against the bearing housing for maximum strength in the vertical direction.
7.13 Optional Modifications to the Main Hinge Design (Spring Quarter) Following the necessary modifications discussed in the previous sections, a number of other design changes were made to the main hinge to allow for an easier and cheaper way to manufacture it. The original design consisted of fourteen separate parts prior to assembling the hinge. It was determined that by making a few changes to the design in addition to those changes required for s1ze constraints, the number of parts prior to assembly could be reduced to ten.
7-36 7.14 Optional Design Change #1 The voluntary modification involved the machining of two parts which were previously going to be made of steel tubes and plates cut to size. The two parts in question are the end plugs which hold the core in place and keep the hinge from falling apart. Instead of using the 1 6 inch tube welded plates which was proposed during the fall quarter, it was decided that a 1 inch diameter steel rod could be machined to the proper dimensions and used in the hinge. In addition, the main hinge sub-group determined that by drilling a hole partially through the flared of each end cap, the bolt head and wing nut which secure the two end caps could be countersunk. This would help to reduce the overall width ofthe hinge significantly.
7.15 Optional Design Change #2 Following these modifications, the mam hinge sub-group was still concerned about the tight tolerances between the three outer collars and the central core, which were to be made from stock steel tubes with standardized dimensions. Although finding venders with suitably sized tubes in stock was not difficult, the sub-group worried about these pieces not fitting together as well as possible. Because the end plugs were now going to be machined, their outer diameter could be matched to the inner diameter of the central core with a minimum of difficulty. It was then suggested that by eliminating the central core and having the end plugs perform the core's duty in addition to their own, the plugs could be fitted to the inner diameter of the three collars. This design would therefore result in a tighter fit between the hinge components, as well as reducing the overall number of components which would be required.
When the design sub-group decided on eliminating the central core, they knew that the end plugs would have to be modified so they could handle the loads imposed on them. In this design, the first end plug will extend though the firsttwo collars entirely and only partially the collar. The second end plug the order to increase the bending stiffness of the new end plug/central core, the shorter of the two end plugs will have an extension which will slide into a hole in the longer one. This final modification will thereby eliminate a weak face to face connection inside hinge. 16 shows the final end plug/central core design.
7.16 Final Hinge Design #2 (Spring Quarter) Following the fo ur major modifications to the original main hinge design, a design was agreed upon. final shown in figure 11, will consist following components:
1. One forward assembly consisting of 2 collars and 2 braces. square collar, used to hold the forward frame member, be secured to 2 rotating round collars via the 2 braces.
2. One rear collar and bracket assembly which will be welded to the rear triangle frame section of the bicycle. This assembly will have 2 separate brackets welded to a single collar.
3 Two end plugs used to secure the collars in place ...
4. One bolt which will pass through a hole in each of the 2 end plugs. The bolt \�;ill be held in place with a \Ving nut and \vasher, and will in turn secure the end plugs and, accordingly, the entire main hinge.
5. One aluminum block used to keep the rear brackets from sliding with respect to each other.
7,17 Materials In order to build the a number of items must be obtained. These items include the following:
7-38 6 L short (< inches) of 1- diameter steel tubing for the three round collars.
2. A short length (< 12 inches) ofa 1-1/2 inch diameter solid steel rod.
3. An 1/8 inch thick section of steel plate from which the four support brackets can be cut
4. A 1/2 inch thick block of aluminum
5. Four 10-24 bolts and nuts
6. One 2 inch long bolt (3/16 diameter) and a matching nut.
7. A 1-1/2 inch length of steel square tubing with an cross section of 1- 1/2 inches by 1-1/2 This will be used fo r the square collar ..
Presently, items #1 through #5 above have been found on campus in late April and were set aside until construction began. The design group later located items #6 and #7 offcampus and of charge.
7.18 Manufacturing Considerations The majority of the work that will be done while constructing the main hinge will consist of cutting and finishing pieces of steel tubing and plate welding the resulting pieces into the necessary components. All machining was performed on campus by the group members, and was done as follows:
1. Cut round and square collars to their approximate final length using hydraulic band saw
2. Cut sections of steel rod to the approximate final length of the central core and the end plug. This was also done on the hydraulic band say.
3. Sand down the square collar to its fianl length using the belt sander.
4. Tum the round collars on lathe until they reach their final dimensions.
7-39 5. Turn the central core and end plugs on the lathe until they reach their fianl dimensions.
6. Cut sections of steel plate to the approximate dimensions of each of the four brackets using the vertical band saw.
7. Machine the brackets to their dimensions on the milling machine. The brackets were machined pairs (first the two rear brackets and
two front ones), which helped to keep dimensions ,....,,,r,.._,...... ,.
8. a the rear bracket support block using the vertical band saw.
9. Clamp the rear brackets to either side of aluminum block and drill four holes through this assembly. Install fo ur bolts to secure this
.fu4:erthe design team completed all the machining listed above, it was time for the resulting components to be welded into place. AU welding was perfo rmed by Jim Surrette.
7-40 f11II IIIn
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I_ ------l
n------. lr---� :------' ! i ��-I -��=-�j - I I ------
. I
--�
Figure -final hinge design 11
7-41 - tV2.{,)N'r co� IJNO I3Y.2Ac,.K.£1 .c�s� i&,v'
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------0-UJI(l � AND �0<£:1' A'$SE.W\!31. 'I ( �)
Figure exploded view of hinge 12 -
7-42 / //�I V
Figure _ roposed lVJ' O ifica"..on o�'Mam . Jo int JJ p · " di 'J
7-43 l
------
Figure - old andnew hinge designs 14
7-44 9.50
. 75 . l '38
¢2.94 ' ' 00 ' 10.2 E 5 +----.....j l. 12 -+----..... I
Figure Location of welding plate 15 -
7-45 l "· · -r� -
- ,______r I '· .... I ,, . I 1"1 1 '1 ' , .. Iz. , ______.. ,
_ _ _ _ : ______: lJ L z 'f1, • ..., S; � ,,�� �,.,··
Figure Final end plug/central core design 16 -
7-46 ··- --
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Figure Aluminum spacer block 17-
7-47 8. Seatpost Joints and Assembly
8.1 Initial Design We addressed many problems m design of the seat post. These problems include:
11111 Overall Strength Seatpost.
11111 Ability to Fold into the Allowable Space Requirement.
1111 to Adapt to DifferentRiders
8.2 Overall Strength of the Seatpost The fo lding compromised the overall strength of the frameo The weak points would be at each of the fo lding joints. the seatpost were one piece, it would be much more stable. The seatpost has to be the strongest member of the bike because it directly resisting the most stress due to the rider. Each bump that the rider must travel over will put a greater stress on the seat post.
The worst possible situation would be that seat post breaking while the bicycle is being ridden. Another possibility would be if the seat post decided to fold by itself. With the ability to fo ld or collapse seatpost, the fear of a seat fo lding is a great concern. That is why the post must be not only easy to fold out but must remain stable while in use.
8.3 Allowable Space Requirement In order fo r the bicycle to fit into the allowed space, the seat must fo ld in toward the main frame. One other consideration was that the overall width could not be over 6 inches, at least not when one folds the bicycle. This constraint would compromise the overall strength. would have to resist these requirements.
8-48 8.5 Re-designing the Seatpost Since the original proposed design, the seatpost has undergone many changes and revisions. In the beginning, support cups welded to both sides of the frame supported seat post A single cup welded to the inside of the seat post beams supported the adjustment post The reasoning for the support cups was for the joints in the seatpost. However with the space requirements, we reconfigured the design. In Appendix D one can see the original seatpost.
The front parts (handle bars and front forks) ofthe bike raised a great deal
of concern when thevJ would not in the allowable soace.• With the seat 'nos t not being able to collapse and fold around the tire, we need only a single joint. We no longer needed the support cups and sliding collars without the extra joints. The present design consists of:
1111 The Two Support Beams
• The Seat Adjustment Member (a smaller tube inside a larger tube)
1111 The Seat post Main ,<\x-J e
111 The Support Plates
8-49 A view of this can be seen Appendix D.
8.6 Support Beams The support beams have changed very little since the first preliminary designs. only major difference is the dimensions. The original cross section of the beams was to be 1 inch by 1 inch. We downsized the cross section to 112 inch by 1 inch. With the length of time a great concern, The cross section went back to original 1 by 1 inch cross section due to having that size at Northeastern ..
The two support bars' length has shortened also. The original design was to fold and encircle the back tire and bike frame. However, the front end of the bike has undergone a great deal of change. More specifically, they shortened the handle bars height. Hence, we had to shorten the seatpost. The shortening was so dramatic that it would fit allowable area merely by folding backward and resting upon the frame. The overall length of the support went from 12 inches to 9 3/4 inches.
8.7 Seat Adjustment Member easiest way to accomplish this part of the design would be to have a smaller tube that can slide inside the main seat adjustment tube. After setting up bicycle, the rider can adjust the seat. To adjust the seat, the rider would have insert a pin through holes in the adjusting post. From this design, we can then drill a hole through the supporting beam. The rider inserts a pin through this part to support the seat.
8.8 Seatpost Main Axle Due to the changes, the seat post will only bend in one place. The joint will be have a 1/2 inch bolt with washers and a locknut to fasten the axle into place. The exploded view of this can be seen in appendix D.
8-50 There will be 1/2 inch holes drilled into the bottom section of the support top of the main will allow the axle the seat post to rotate back. A support plate will butt against the frame when fo lded and upright. Appendix D shows this more clearly.
8.9 Support Plates
overall strength. The overall view shows the locations of the support plates (appendix D). The support plates are 1 inch by 3 inch with a 1/8 inch thickness. The top four will around the front and back of the seat post. We will weld the plates directly to the adjusting member and two support members. This will keep the adjustment post from breaking.
The second support plate will surround the around near the bottom of the seat adjustment post. Both this plate and the top most plate will take all of the riding induced moment stresses. They will be both welded to the frame and be each made ofheavy 114 inch gauge steeL
Third plate is to keep the seat adjustment post from sliding all the way through during adjustments. The overall seat post strength will come from the other plates. Appendix D shows the dimensions and design specifications.
8.10 Turnbuckle Attachment Hardware
We will attach one end of the turnbuckle directly to the seat post by use of aluminum hooks. They describe the hooks in the turnbuckle section. The hardware to fa sten the hooks will once again be bolts and nuts with washers. We will drill four 1/4 inch holes through the lower plates for the seat adjustment post at 1/2 inch spacing with a pitch of 2 3/8 inches. The bolts have a counter sink allowing its head to lay under the surface of the hook face. The nuts have nylon inserts to make
it
8-5 1 8.11 The Upright Locking Bolt The addition of this part came as a result of a concern for overall bicycle stability. Originally, the seat post would not be free standing. The turnbuckle would be responsible for keeping the seat upright. With each bump the road, the entire stress will end up on the main We then came up with the a locking bolt.
We will drill a 3/8 hole 2 1/2 inches above the bottom edge of the main support bars. The hole will be centered and allow the bolt to ride across the top of the frame. This bolt will assist the turnbuckle assembly to help keep the seat post from folding backwards while riding. The nut for this bolt will be a wingnut and will only need to be hand tightened to secure
8.12 Economic Considerations To keep down the cost of the bicycle, we will use standard parts as much as possible. The support members all be using standard size steel tubing with standard size waH thickness.
Time is another constraint Bearings and other lubricating surfaces are easy to get There are countless numbers of companies that provide and stock these parts.. By stocking these parts, ordering time is much quicker than if the had to order them from their supply houses. The seat will be a standard bicycle seat \Vith no special qualifications.
8.13 Dimensional Control The seatpost has never had a problem with fitting into the allowable space" With the current design, it takes up less room than it has ever. This has benefited the rest group by giving them even more room.
8.14 Mechanics/Strength: Many calculations have been made to insure that this seatpost design will meet the space requirement but also seatpost will not fail
8-52 ride. Between the plates and the heavy gauge tubing steel, each component will have a factor of safety of at least 2. These areas include:
1111 The Overall Strength
• The Seat Post Axle
1111 Support Plates
8.15 Overall Strength The strength in the seatpost mostly needs to be resistant to collapsing downward while standing upright. real strength come from the turnbuckle support. turnbuckle is mentioned in part of this report in clearer terms. However, the turnbuckle cannot handle all strength and support problems. One example is the strength in the axle.
8.16 Seat Post Axle The axle will have at least pounds coming down upon it at the two ends. The shear stress coming down will be crumple a rod that is not strong enough. With this reasoning, the diameter of the rod has to be at least 3/8 inch or it will crumple.
8.17 Support Beams Another section of concern is the seat adjustment member maintaining its position between the support beams. theses pieces were merely welded together, the entire stress would be acting upon the welds. The welds would hold up for only a short time before failure. With the addition of the support plates, the main stresses will be relocated away from the welds. The stresses will react against the material of the plates thereby saving the welds.
8-53 9. Overall Design Considerations
9.1 Drivetrain Design The function of the drivetrain system for our design is to transform, transmit, and control power supplied by the rider. The drivetrain system that was chosen to transmit power from the rider was a standard chain drive found on many of today' s bicycles. Chain drives combine some of the more advantageous features of belt and gear drives. Chains provide almost any speed ratio for any practical shaft separation distance. Compared with belts, chains offer the advantage of positive ( no slip ) drive and therefore greater power capacity.
In its simplest form a chain drive consists of two sprockets of arbitrary size and a chain loop. Sprockets are wheels with external teeth shaped so that they can into the links of the drive or driven chain. The term chain drive therefore denotes a combination of chains and sprockets and the particular way they are mounted to the shaft. In the design the bicycle group is working on, the sprocket size that is mounted on the rear tire ( drive sprocket ) is 1.5 inches, and the sprocket size mounted between the pedals ( driven sprocket ) is 6 inches. These particular sprockets will be of standard sizes according to ANSI specifications and will be bought froman outside vendor. See the figure 18 for more details.
9-54 Drive Sproket
sprocket diagram 18 -
Chains transmit power through mechanical interlocking of the driver and driven sprockets. The driven sprocket is forced to rotate under the constant tension imparted to the chain from the driving sprocket. A principle advantage of chain drives is their high load capacity, which results from hardened steel links being loaded in simple tension and having many teeth engaged in the sprocket to produce no slip conditions. Chain drives are thus one of most compact, powerful, and efficient designs fo r transmission. This is the main reason why the design team didn't try to develop a alternative drivetrain system such as a belt drive or complex gear system.
In these particular type of transmissions, to achieve an optimal speed depends primarily on the gear ratio. The gear ratio is a simple ratio of the diameter ofthe driven gear ( driven gear ) to the diameter ofthe drive gear (drive sprocket). In order to achieve the maximum speed out of a chain transmission system, the diameter of the driven gear must be larger than drive gear. Our particular design was based on experimental calculations modeling a bicycle with a selected gear ratio 4:1 using a 12 inch rear tire. This is equivalent to a 1 ratio on a mountain
9-55 Standard calculations velocities attainable for this bicycle based on the selected gear and ( angular velocity ) have been calculated for this project. The values fo r crank angular velocity are between 40 to 80 rpm based on the estimations that these are the average values for an average non-trained individual. To come up with a proper ratio fo r the rider also involved selecting one that didn't require a great amount of energy. Based on these facts, the optimum gear ratio that wouldn't require the rider to over exert themselves was the 6.5 to 1.5 inch ratio.
Table -gear ratio selection 2
· Gea:rRatio Selection
CL CV VD
6 1.5 12 5 40 8 603 1.9 5.7
------...... - ··- ...... ------················--·· ... 6 1.5 12--·-····- 5 ------60 8 9047.8 ...... 8.6. . . . 6 1.5 12 5 80 8 12063.7 6 2 4523.9 4.3
6 2 ··········-···-·······-···-·····-·-·--·-·····6785.8 6.4········----- 6 2 12 80 8 9047.8 8.6
...... ,. ... - ---··········· ...... 8 ·--•«••·········--···1.5 12 5 60 8 12063.7 11.4
•.• ...... 8. ... 1.5 12 5 80 8 16084.9 15.2
Reference table:
...... �.� .:.X�<:>�t ..�P�?.�� ��.��I?.e.�e..r...... ················· ... . . � ········ ··· ····· .<=..�.: . �.r.a.�..�
...... ��: ...... �� �.�and.?.P..��. Tire�.�.e. diameter�.. �.��.f!.le.� �� ...... g. Y� g.�.a.�. . A?.�.r..Y�!:..
Another valuable aid in the selection process of the gear ratio was the overall design and location of the rear triangle. If a larger gear ratio than 6.5:1.5 was to be fitted on the bicycle transmission system, the rear triangle would have to been modified in order to install a larger sprocket A larger sprocket would have come in contact with a certain member of the triangular frame that is connected to rear hub. To accommodate a larger sprocket to increase the gear ratio, it would have necessary to redirect a connecting member over the gear, thus effecting the overall strength of the triangular fr ame.
9-56 Based on the configuration of the rear hub, the fianl drivetrain design is a direct drive system. This type of system allows us to use the least amount of parts possible, and requires the least amount of space to be taken up within the rear drive shaft. Due to the configuration of the rear triangle, the rear hub assembly for our design was confinedto a small space due to the fact that the rear tire had to be such a small height. The small hub space that we were given to work with was the main factor that would require us to use a direct drive system
The following is a sample testing done on a similar drivetrain, quoted the design group responsible for the drivetrain design:
Although we have the option of changing the rear sprocket to get a higher gear ratio we felt that in order to be sure if the gear ratio selected is acceptable, it was necessary to do an ergonomic test. Again, the ratio of the front sprocket to the rear sprocket for the design is 1 (or 6. 0 to 1.5 inches ) with a 12 inch rear tire. Since the bicycle thus far is completely mathematical without a physical model, a study was conducted using a mountain bike ( TREK 750 ) which has twenty three inch tires. This 4: 1 ratio with a twelve inch rear tire is approximately equivalent to a 2:1 ratio with a twenty three inch rear tire. Using the TREK 750, one of the group members rode it in the 1 ratio for approximately forty minutes.
The purpose of this test was to double check if the researched information was valid for our bicycle gear ratio. The member rode the test bicycle for an estimated time of forty minutes a 2:1 gear ratio at all times. A speedometer, not calibrated, was attached to the bicycle to provide readings the actual speed. The rider was able to comfortably maintain the 8 miles per hour over various types of terrain ( up small hills, rough roads, and on sidewalks ) . The conclusion of this test was that the 6 inch front sprocket to a 1.5 inch rear sprocket will be acceptable.
The following information was gathered about angular velocity and horsepower. :
9-57 Ta ble - velocity considerations 3
Questions arose about the forces applied to the pedals and whether these forces were unreasonable. The physical test provided an answer that resistance force of the pedal was minimal when starting off became easier as the rider pedaled faster, as would be expected. numerical numbers were obtained while test bicycle, therefore the results of the physical test may not be applied to aU individuals.
9.2 Triangular Frame Assembly The function the frame is to enclose, restrain or support the integral parts of the assembly. The frame is also backbone the structure whose essential parts have been put in their proper places and secured together. In the case of the collapsible bicycle frame, the role of the frame is to provide support or alignment to the extending structural members and rotary bearings located inside the wheel hub. For the bicycle design that is being worked on, the fr ame has to accommodate mobility and the ability not to be in the way folding members of the bicycle. The frame chosen for the design has a very interesting geometry about it because it doesn't resemble a traditional style of bicycle. Connected to the triangular frame assembly is the rear tire assembly, the pedal and sprocket assembly, and support for the seat. Hinges are located at the bottom right of the triangular fr ame to allow the member connecting the fr ont assembly of the bike to fold back, and at the top of the triangular frame for the seat post column to fold back. See figure 19 below.
9-58 Top Triangular of Tria..11glular Frame Frame
•
Bottom Left Bottom Right Rear Tire Assembly Area Pedal Assembly Area
Figure - rear triangle 19
A well designed frame is essential in our design case because it determines the quality of the ride and how the bike will respond to various conditions encountered on the road. The frame must also be able to cope with all acting forces. In the case of the collapsible bicycle frame it must be able to withstand a wide range of fatigue in its life span. The human factor plays a large role in the design of the frame.. The triangular frame assembly has to support the maximum weight of a 250 pound commuter. It must also contain the forces supplied by the crank assembly, the moment forces added by the main cross member of the bike, and all the various tension forces that are applied by the action of pedaling the
triangular frame represents the only rigid member on the bike. It was designed in a way to withstand all the stresses acting upon it, but also in a fa shion that made it as compact as possible. The rear triangle is basically a right triangle with dimensions of 13 x 11 inches and a hypotenuse of approximately 17 inches. The triangular fr ame assembly is actually comprised of two parallel triangular units of the above geometry. The rear wheel will fit in between the two triangles. In the location of the triangular fr ame, where the rear tire assembly is located, two parallel triangles be separated by 5 inches to make room for rear to
9-59 in between. two bottom members of the triangular frame will be machined in a fashion to not to come in contact the geometry of the frame.
The material selection according to the subgroup in charge of designing the assembly was easy to determine due to the "robustness" of the rear triangle assembly. According to the constraints imposed by the forces on the bike, there was a large pool of materials that had credibility to chosen for the job. Most of these materials consisted of various kinds of metals. According to the best overall design considerations, the material which has the bets characteristics for the design is a chromium alloy steel ( cro-moly ). reasons this material was favored over many others was because of wide proven use the bike industry and of the physical properties that the design group found that it possesses. One candidate from the chromium metal family is a grade which possesses the tensile strength of 89,000 psi, and has a yield strength of 62,000 psi. It's machinability characteristics has it rated as having a machinability percentage of 57 %. Most of the chro-moly metals that were researched, had similar mechanical properties.
9-60 The concept folding bicycle presented this report is very unique and satisfies of the stated design objectives. Discarding idea of a regular everyday bike was the biggest obstacle to overcome the design. Input from all of the members of the design group has been taken into account and incorporated into the final design. We feel that our design uses some very well engineered components and we are confident that it perform up to its expectations.
Work progressed a satisfactory pace throughout the life of the project A complete working prototype of the bicycle is complete for demonstration purposes. The protoype demonstrates that our design works as planned and work would be necessary to the bike. One area that would definitely need to be explored further is weight reduction, but since that was not one of our initial design constraints, it was neglected up to this point. It should be taken into consideration that the prototype model of the bicycle was constructed largely from scrap materials and old bicycle components at a cost of less than $150. A true prototype would involve much more work but is really beyond the scope of this project.
All members of the various design teams provided valuable input and the bicycle that is presented in this report truiy is the combination of eleven indivduals thoughts melded into a final design. This project has been a valuable experience for all involved.
0-6 1 111 j_ j_,
Bicycle Bills Allston, MA
Back Bicycles Boston, MA
J Bromptom Bicycles London, England 11-62 Appendix Directory Appendix Concept Designs Appendix B Optimization Report for Main Support Bar Appendic C Main Joint Drawings Appendix D Seat Post Drawings Appendix E Overall Design Considerations Appendix F Project Schedule Appendix G Calculations 12-63 Appendix A Concept Designs OVERVIEW OF CONCEPT DESIGNS Designs with the GA designation were presented by Professor Adams' group and the designs with the GK. designation were presented by Professor Kowalski's group. Sketches of all the concept designs can be found in the appendix the report. Concept Design GA-1 This design was developed by aiming to reduce the width of the general area around the bottom bracket to six inches. current width on a standard bicycle is six and a half inches not including the pedals. This design will reduce the width of the bottom bracket by having the drive train and sprocket go through the center line of the frame. Traditional bicycles have the drive train and sprocket run along side the frame. The frame has a rectangular cross sectional geometry. This cross section was designed to reduce torsional forces that might be experienced, and to add strength to the bottom bracket. Foldable pedals would be required to bring the overall bottom bracket width to six inches. Also, the rear wheei has the drive train in it's center which would require that there be two thin wheels on either side of the sprocket. The front portion of the bicycle was substantially different from a standard bicycle also. It involved having a steering column connectedto two front wheels, eliminating a fork. Advantages Width is reduced substantially illi There are only two pieces 11 Disadvantages The bottom bracket does not seem as though it would be able 11 to support the 250 lb. load Does not easily fit into the required folding dimensions 11 The two wheel front end wouldcause stabil ity problems in 11 turning and would increase the turning radius Many parts would need to be custom made, such as the rear 11 wheel Design GA-2 and These two designs were so similar the description wi!! be combined. This concept retains the general geometry and workings of a standard bicycle but is reduced in size and has a folding mechanism that allows it to fit into the required dimensions. The rear triangle of the bike becomes the main support and everything is built off of it There is and extended seat post which brings the rider height to a comfortable level. The top tube the bike is attached the seat tube with a hinged joint and is telescoping, while the down tube is removable. The handlebars are similar to the seat post that they are extended to provide a comfortable riding position. To fold the bike the removable member is taken out and the entire front of the bike is brought toward the rear with the telescoping top tube also the front tire removed. Once in the collapsed state the top tube is brought down be parallel with the seat tube and the handlebars are also folded parallel to the seat and top tubes. When in the folded position, the front fork will straddle the rear wheel. The seat may either be removed or brought down to it's lowest level. Advantages • Retains standard bicycle geometry Uses mostly standard parts and would require little custom • design. Simple folding process 1111 Three or four (depending on seat) pieces 1111 Disadvantages Seat and handlebars would have to be very long to retain rider • comfort. Where to put the front wheel when the bike is folded. • 1!!1 Designing to fit easily Design This design consists of approximately removable parts and a number of hinged components, all of which are based around the 12 inch rear wheel and triangle subframe assembly. The removable parts will include the front wheel, the hand-grip cross member on top of the handle bars, and the support member connecting the seat post to the forward frame. In addition, one or both of the foot pedals may be removable but that has not been determined at this point. The main section of this bicycle design is the rear wheel / triangle subframe assembly, to which all of the hinged components, such as the seat post and forward frame, will be attached. fold this bike, the following steps must be followed: 1. Remove the front wheel (using the quick release latch). Remove the support member connecting the seat post to the forward frame. 3. Remove the hand grips from the handle bars. 4. Fold the handle bars backwards towards the seat post until it is almost parallel to the forward frame section. Fold the forward frame (and handle bars) underneath the bicycle until the two parallel bars which make up this forward frame section straddle the rear wheel. 6. Slide the forward frame section through the collar (located at the hinge) in the direction of the foot pedals. It should slide approximately 7 inches before it cannot slide any further. lift theseat up until the base of the seat post frame is released from its supporting collars. 8. Fold the seat post as shown in the attached diagram. 9. Secure the front wheel, support member, and hand grips to their associated locations on the collapsed bicycle. Advantages Unique joint design allows folding without sacrificing strength 111 or three pieces 111 of assembly 111 Disadvantages Custom designed joints = Length of handlebars. • Width of main folding joint • Design GK-1 This idea follows classical bicycle frame. By separating into five distinctive pieces or areas the bike is fitted into the allowable folded dimensions. A locking device connects the handle bars and fork. The chain drive, back and back support will stay as one piece to minimize assembly time. slotted groove or dovetail type of sliding mechanism on the back assembly connects itself to the support bar also, the seat slides into the top part of the support bar. The front part of the support bar will include the locking hub for the handle bar and front fork. Finally, a cable will add to support to the frame. Advantages It will require no tools to assemble the bike • The bicycle is ergonomic for different sized people. • Disadvantages • Too many separate parts The locking hub would have to have a great deal of strength. • Misalignment in the locking hub that would cause serious • problems. The slotted groove may jam if dirt collects or a misalignment • during assembly. The main portion of strength relies on the groove and locking • hub The area to fit the bicycle was the driving force behind this idea. The main part of the frame will conform to the necessary dimensions. By using a double chain drive a high gear ratio and speed can be achieved. This design would provide comfort for almost any sized rider since it is adjustable. The only parts that detach during disassembly would be the pedals. There are three major pivot points; one is for the front fork that will be folding in onto the frame. Telescoping front forks will also be used so that the length can be adjustable. The second is for the seat post which will fold down onto the frame. The last pivot point will be at the second gear of the double chain drive and will consist of a locking that will support to the back member. When the folding begins, the gears will pull away from the hub which will unlock the hub causing the member to be rotated into the frame. The gears wouldnot only drive the bicycle but also provide a great deal of support. Advantages The compact bicycle can attain great speed. 1111 Size of wheel can be small since the gear ratio is high • There will be only three separate parts, two being the pedals • All members wouid haye a great deal of adjustability. 1111 The height of the frame will not limit the crank size. • Disadvantages The bicycle will have a high center of gravity with the raised 1111 frame. double chain drive will cause problems if one chain fails. 1111 The locking hub at the end the bike would have to be the 1111 strongest point. Machining costs will be high to design the double chain drive. • The front fork pivot point will have to be over designed to not 1111 have fa ilure. weight on the front fork cause a high moment. Appendix B Optimization Report for Main Support Bar Problem Statement Choose an appropriate aspect of the design project which is for optimization and perform the optimization. Description of Optimization The optimization will be performed on support section of the of the collapsible bicycle. By modeling support as two 1.125 outside diameter steel tubes with a variable inner diameter as a simple cantileverbeam a bending problem was set up. According to the collapsible bicycle design parameters, maximum weight of the rider is 250 lbs. The support member will experience a 125 lb force at A standard cantilever beam bending stress equation be used and is shown as equation 1. My 1 I addition to bending stress the weight of the support will considered. An expression for the weight per area is given in equation 3. equation 3 The optimization problem will minimize the weight of the cylinder and the bending stress experienced by the cylinder. Since there are some physical limitations of the system we win set up the following constraints: d1 s; 1.069 in constraint 1 30,000 psi constraint 2 O'max S: Constraint 1 was chosen because that is the largest inner diameter available and the maximum bending stress was chosen by findingthe yield stress of steel and using a safety factor of slightly less than two to provide for such things as impact forces. A diagram of the modeled beam is shown below in figure 1. 1------11 in -----1 I F= = 1.1 VIeW 1. Finally 1 = ---- +a·W 4 vbend optimization was performed Microsoft using the function. This function allowsthe user to either minimize or maximize the result of an equation by changing variables in the equation. The results and problem set up are shown below. 0 in. 0.488 in. a=80000 Appendix C 1\tiain Joint Drawings �-�f:. !I\IIC,.,X IVVIVVV' w' '150 lb:� . t I : "' l R ff,"C.- rc:.o--c..J., '"" u4 ./1,� rc .-;.. ...- (p'-".,+ A) "'"'"'' 1:. .. . c.. -e. 1-1-1- (" v.c...+I VV'I .( "'""w �e.- ""ww o ::: ::: ::: + +!,.-e ..(,'c.,...,+ VI V'l\11 wk::::t.-l 000 ll'lOO (e'-'"'-1- 13 1 -<"< �. 1<,. : \tJL, (.,."I. !....-, -:: 5 ; .. . Lt � 30 i ... . r:z, , ZO 'S"- 3 lbi . "' """ ...... "' ...... :::l:..... :t:t..... "' """ 000 V\00 - !'< -<"<1 qq C'Of' F c: r Tf, -:., t ((. c.f +t, -e.- i"rvvrf £.-£.:. ( R._ ) (CAvieS Gt VVl 0 V\.-'1 e.""'+ C,\J -f[,e v-�C"-e- ./-[.-(_._ L;,._,,v- c.."d vlicVv ber ,-\ ',-· ) pu•V1f I I .{;CAY\-� I l-;cc.-v'S V""CA'·l· ;� fue- (C-V.r f� {-£_ A). I GA,/Ij ( P";VI+ -- <--· r .J_v ctc r {_c_,vVl-1-cr� + '1/'(.,VV"�Vl-�- ) u. -:;.,-- c t:- -/-(..., I • tt� -- ( F ) ,,/, � l L/\.,..•�!V"\-t'G._ ,Vi"C.. J) -s ' oJ . 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'10 b· : / ' � � ' i F A A� L{[c C.v-s-s - -s:::d'"VloI c;.v-e,c;_ cJ" (.c.,r +- (.;:,.,, -�::.-<.-�-··""""'1 O.• t.J:A. t::_V'cY p <..J e) ( cJ' I d Vlln VI t) rrg(J.7'5 , )'"l :. 0.675 1 i111 t...... 71 (12'1:.- ,. ... r-(Q.Gt6 , ...... ::t::t:t:...... """ "' 000 7T[(u.S'fs7 y·J O.t1C/3u ;..,., z V>OO ;...,y - (u.'-l7s5 ... -f'< ..v") _)' •. I. Z5 ______o_ :_P ---1 ------"� ------A ______------+------4 ------ - - �------) ------· ------J( "J ------_.,.,...... ,., � 27 (-- ocx_;;-- --I b-.,_s ------ ------_. _� r- o s o CJ.Z.."' ,, ------4---- . ------· -- c 'X;) " ' ------·------ "'- - ______· _ ,.., _ _ � _p __ _ :_ ZL.Y O O_l� ------ ------ · ------ ------Appendix D Seat Post Drawings T�t \2-�N�\"·-�- ..::.., ,f �t:.ss :·o �:?. :.-<:. S�:. ;:..·· ?o;-,1 I L lZ E. ! "S H1 e •;: 0 .Lt.. 0 W 11"4e.� Vl lll ll'l ...... "'"'"':t:X::t 000 11'100 -N -N"l' "1<1'"1 --- NNN f_.lc,.� q ( ) �-.� E �"' 1 \::. \AG'�,· .U-1 � ) Ot= AX Lt FCR ':Ct.:.,·\PC:, i ie ' {hidne�;, � 0.101 w te O.lOl (l/?:J"i . 11 1 1v\ � l 11S )( 0.0\V?.� " d Q,'!:lQ \ I,I),J 7 T '81:i. S h::r•n / .j,n c, �L -� ,-�� �-�- ��-;�)___ _ _ l1(0.c.)O in Y" ( 0, 0'6(;;:, in > MAx 1 Murv, 'be."'' D' NG ':.>> 1.:::.�,. s INDuce t:> \.;t-.J ce.�-n o::.l( ::,\,,",>(;'<;.'\ !:JAR A-� •2- zso"�;, ::. 'iS�·:,·:,� 1 � ( -- -- ·------ftfi (� ,, e, J- � '1 1 � - � !. I '1 ( ) ( .. lS i ( J!S).3 "":: o.os1 '{' 12 -· (' I" I/2. Q.S 11' I o.crs 11 -t- '!-/' 1 >nc K WALL 'lz 'l CROS::) -Sf_C! iO>� C.>F f\LLE:i �;,J C:.L::;, ,, ., , :,_' r \JE.><_ I\ ( ;._L �U\'' I"'C';Rl lv\ E.M �t-f< )(\<;:_ ('00-'XIN\\.AfY"\ 5heor �tre :·:. cc, th(; fo1 2 oc h ,:- Ide �� the 1 o ;;-<.! \ -.� "' I oo d on eC>c,, �i0',) \..: -- z c::: o�' /') ( 'I ;:;,o.'6 I::., ,._. Explode View of Bolts o.nd Ho.rdwo.re 3/8. I I I I L __ _ _ _j bolt u;::�· inch Length 3X 4 Mo.in cycleBi FroMe Seat Post Layout Sco.le:112 All diMensions in inches 1 .. X t• steel tubing 5 112 inch leng th 1* ><: 3' stock <118" thickness) 5X 1• steel tubing dio. 9 3/4 11;-I 6 ,__ 1 112' dio. r 2 112 1 5 / 8 _j___ l Appendix E General Drawings --�.....:..______-----�------�- u lU 1------A 1- B C ----1 ,-.- 1------ r------ 1------ lilllllil!ll r------llili!l!l!ll 0.38] D '------' -'- SEAT FRONT A 1.125 2.00 B 0.50 1.00 c 0.75 1.00 D 2.00 3.00 . 7 5 - �--=-- ' l13.3 8 1J� \ · 4 5. o o \ r-- 6.00 5.45 I I . 00 ------1 SCALE 0.333 .50 F. 151 - -, .k--- -r 1 9.50 . 75 . 38 l__L n ------2.94 ¢ 1. 75 f-.----- I 0.2 5 -----1 � ¢ -II.72 ------i SCALE 333 (1'1 (1'1 co -- 1-- LLl 1-- � LU L.J � c:::J L.J OL c:::J []_ OL (_./') o_ (..../) 1-- ::z: OL c::J ....:::::c: 0.::::: LLJ LL DL: � '&. ((f- C) ..,...... _... ...... ----. Appendix F Project Schedule ------� Spring Senior Design Project 1996 �------�-�------�----�------,------�------.------�- 10 Task 515 1 Sorina Quarter Design Project ------· ------t------2d 2 expectations for future work 2d 3 _____ ,___ �--·----- Finalize design of bike 4 Prepare schedule 5 3d -- - r-----t------Ill Finalize manufacturing drawings 5d 6 � ------�- - detailed purchase list 5d and manufacturing i-\ssemble first prototype 2.5d 9 Test prototype 10 and operation 11 ------�-�� 1\/lake any necessary 12 -- --- Assemble-- final product 13 Make any final changes 14 Prepare executive summary 5d 1111:o!lnmtm Prepare midterm report and presentation 5d -�-�------�- Midterm presentation 17 4d �· ------�-�---- Prepare final report and presentation 7d - 111 . Final presentation 2d ' 19 Project complete Od 20 --!.·�� Task - Rolled .....- ----.....- Rolled Up Task __ ••••- Rolled Up Milestone 0 Appendix G Force Calculations F;_ r;., I I F.s / { ( '' � H ):: L-r x i j"' � I I ! 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FORCE.XLS : i i i i i i Forces While Pedaling (lb's) i i i Riders Position i I Standing Leaning ! iStraight Up Forward %load on ! 20% 30% 40% 50% bars 1 Max Arm I 45 30 15 0 Force Angle I I I FHx :::!1 35.36 37.50 I 25.88 0.00 37.50 FHv =] 35.36 64.95 96.59 125.00 125.00 I i , Fp I 200.00 175.00 I 150.00 125.00 200.00 l:::i I 1 F1 i=J 83.91 102.02 121.86 1 138.98 138.98 F2 l=i 166.09 1 147.98 . 128.14 111.02 166.09 1 I I I I I I I I I : I l I I, : fi, c 1 l\ uSSOrt�e_c9 JJo-+c H 4 \'esc V:f �-: hH X � fo be cJSO 16 s- 1 1-1 �oi� J>,·f c. c·h ovtS / 1 J I .: (_ '{L"-- ( - . 7 C ? 1 I r-1 - ( r� .:- 1 1 ...:. 'v.: .,; \. � 1'(-J. I \{,iv)' :- -: I �73 \'�/$ _ _ ;r-J t.(c < r 1 c; c 3cc tl� -: oD t!� -:: 6 co1Aj"i C'-1T ,o r 1 /,' r, l'i/ lb L� ��"r. 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