UNIT2.6-Mechanisms: Eng Notes

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EP@BHS-TOPIC 2: Energy, UNIT2.6: Mechanisms Page 1

UNIT 2.6 MECHANISMS:

Concepts Addressed in Lesson: 1. Most mechanisms are composed of simple machines, interlocking gears, chain driven sprockets, and belt driven pulleys. 2. Mechanisms are used to transmit energy through a system by manipulating force, speed, and direction. 3. Mechanical advantages mathematically represent the ratio of the force output to the force input for mechanisms.

Performance Objectives Addressed in Lesson: It is expected that students will: o Measure forces, speeds, and distances as related to the operation of mechanisms. o Distinguish between the six simple machines, their attributes, and components. o Calculate ideal mechanical advantages, gear ratios, and drive ratios for mechanisms. o Design, create, and test gear, belt-pulley, and/or chain-sprocket systems. o Calculate work, power, torque, and efficiency for mechanical systems.

Assessment: Explanation • Students will explain the difference between engineering and engineering technology. • Students will explain the relationship between work and power in a mechanical system. • Students will explain the processes of calculating mechanical advantage. Interpretation • Students will make journal entries reflecting on their learning experiences. • Students will explain the importance and relevance of simple machines in everyday life. Application • Students will apply their knowledge of simple machines and calculate mechanical advantage of objects within the lab environment. • Students will apply their knowledge of system efficiency to calculate efficiency of a mechanical system. • Students will apply their knowledge of gear, sprocket, and pulley systems to calculate speed, distance, rotational direction, and mechanical advantage. Perspective • Students will select an engineering or engineering technology field of interest and prepare an interview with a professional within the field of interest. • Students will identify and discuss the role and impact of simple machines, compound machines, and gears, pulleys, and sprockets throughout the development of civilizations. Self-knowledge • Students will be required to reflect on their work in their work-guides • Students will conduct formal periodic self-assessments of course knowledge and content.

Essential Questions 1. Why is it important to begin considering career paths during high school? 2. What career opportunities are available to match your specific interests? 3. What are some current applications of simple machines, gears, pulleys, and sprockets? 4. What are some strategies that can be used to make everyday mechanisms more efficient? 5. What are the trade-offs of mechanical advantage related to design? 6. Why must efficiency be calculated and understood during the design process?

Date Completed: Preliminary Final Grader Name: Initials: Grade: Grade: Initials:

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A. Simple Machines

We will begin this lesson by consulting the Merriam-Webster Dictionary to obtain a specific definition for the field of “mechanical engineering”:

It is apparent from this definition, that mechanical engineers must understand the fundamentals of tools and machinery, so let’s now use the same dictionary to explore the various definitions of “machine”:

For our current purposes, the most important definition listed under “machine” is 1.e(1): an assemblage of parts that transmit forces, motion, and energy one to another in a predetermined manner (2): an instrument (as a lever) designed to transmit or modify the application of power, force, or motion. Which requires definitions that build a bridge between force and power:

Force – A push, pull, lift, press, etc. (MKS unit is called a Newton (N): 1 N = 1 kg m/sec2)

Work – The increase or decrease in the amount of energy in a system by the action of a force through a distance (MKS unit is called a Joule: 1 J = 1 N m)

Energy – The measure of system’s ability to affect change in itself or the environment (MKS unit is also called a Joule (J): 1 J = 1 N m)

Power – The rate of work or energy with respect to time (MKS unit is called a Watt (W): 1 W = 1 J/sec)

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A simple machine is a device which converts a work input into a useful work output through one of six basic mechanisms, as shown in the illustration to the right. These images follow the convention that the input is referred to as the “effort” and the output is referred to as the “resistance”

From the images to the right, it should be evident that a simple machine can multiply force such that Fr is greater than Fe. That is, a small input force (Fe) can accomplish a task requiring a large output force (Fr). But the constraint is that the small input force must be exerted through a larger distance so that the work input is equal to the work output. You are trading a small force acting through a large distance for a large force acting through a small distance. This is the nature of all the simple machines above as they are shown above. The factor by which a machine multiplies the force is called the "mechanical advantage".

(Source: http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/simmac.html#c1)

For ideal machines, would be no energy loss within the system, the work output will be equal to the work input, and the machine would be 100% efficient:

Ideal Machine: No energy is losses occur within the machine Work Input = Ideal Work Output Efficiency = 100% Ideal Mechanical Advantage (IMA) = Ideal Output Force/Input Force

For real machines, there will always be some factors (like friction, flexing, etc.) that will convert some of the energy input into non-useful (thermal) energy. This results in the useful mechanical energy output being less than the mechanical energy input and causes the actual mechanical advantage (AMA) to be lower than the ideal mechanical advantage (IMA):

Actual Machine: Energy losses occur within the machine Work Input > Actual Work Output Efficiency (always less than 100%) = Actual Energy Output/Energy Input Actual Mechanical Advantage (AMA) = Actual Output Force/Input Force

Simple Machine Examples Directions: The following pages include background information on each simple machine and space for students to document an example of each in detail, by utilizing a variety of provided materials from which to construct simple machines and responding to the associated prompts. Students may work together in groups of their own choosing. Students will be provided with a variety of tools to measure associated lengths and forces.

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Lever - consists of a lever arm and a fulcrum. Effort (Fe) is the input force which must be supplied Fe Le Lr Fr by the user or an engine of some kind. Resistance (Fr) is the output force which is also the force resisting motion.

MECHANICAL ADVANTAGE: 1. IDEAL MECHANICAL ADVANTAGE for a LEVER

ideal mechanical advantage (IMA) = Length from fulcrum to effort = Le Length from fulcrum to resistance Lr

2. ACTUAL MECHANICAL ADVANTAGE for a LEVER

actual mechanical advantage (AMA) = Resistance = Fr Effort Fe

Types of Levers First class lever: the fulcrum is located in the center of the lever arm and the effort and load are at opposite ends. Example Seesaw

Second class lever: with a second-class lever the weight is located in the middle and the fulcrum and the effort or at opposite ends. Example Wheelbarrow

Third class lever: the effort is applied at the middle of the arm and the weight is held at one end while the fulcrum is at the other end. Example Elbow Bending

First Class (see-saw) Second Class (wheel barrow) Third Class (catapult)

NOTE: Label important quantities on diagrams: Fe, Le, Fr, Lr

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 Lever Example Documentation: Perform the following: • Sketch the lever • Label the effort and the resistance • Measure and label quantities necessary to determine the ideal mechanical advantage • Calculate the ideal mechanical advantage • Measure the effort and the resistance associated with using the lever to support a load • Calculate the actual mechanical advantage

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Pulley - A single pulley simply changes the direction of a force. When two or more pulleys are connected together, they permit a heavy load to be lifted with a smaller force. The trade-off is that the end of the rope must move a greater distance than the load. Fixed Pulley Moveable Pulley Block & Tackle

NOTE: Label important quantities on diagrams: Fe, Fr

MECHANICAL ADVANTAGE: 1. IDEAL MECHANICAL ADVANTAGE for a PULLEY

ideal mechanical advantage (IMA) = number of strands supporting the resistance

2. ACTUAL MECHANICAL ADVANTAGE for a PULLEY

actual mechanical advantage (AMA) = Resistance = Fr Effort Fe

Fixed Pulley: The pulley is attached or fixed to a strong member, which will not move. When a fixed pulley is used the force needed to lift a weight does not change and the rope must be pulled the same distance as the weight is lifted.

Movable Pulley: The effort needed to lift 180 pounds weight is 90 pounds. The mechanical advantage of a movable pulley is 2 and the rope must be pulled twice the distance the weight is lifted

Block and Tackle: A system of multiple pulleys. It reverses the direction of the effort so that a downward pull can be used to lift an object. For the example above, the mechanical advantage is 3 so that 40 pounds of effort is needed to lift an object weighing 120 pounds. (The distance of the rope pulled is tripled.)

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 Pulley Example Documentation: Perform the following: • Sketch the pulley • Label the effort and the resistance • Measure and label quantities necessary to determine the ideal mechanical advantage • Calculate the ideal mechanical advantage • Measure the effort associated with using the pulley to support a load of 9.8N • Measure the distances moved by the effort and the resistance as the load is lifted 10.0 cm • Calculate the actual mechanical advantage • Calculate the work input, the actual work output, and the efficiency

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Wheel & Axle - similar to a rotating lever. The wheel and axle can also Wheel & Axle be used to change from rotary to linear motion. By increasing the diameter of the wheel, the linear distance traveled for one revolution of the axle can be increased. A wheel & axle can be made from a 2nd or 3rd class lever.

MECHANICAL ADVANTAGE: 1. IDEAL MECHANICAL ADVANTAGE for a WHEEL & AXLE

ideal mechanical advantage (IMA) = Radius to` Effort = Le Radius to Resistance Lr

Fr Fe

Fe Fr

2. ACTUAL MECHANICAL ADVANTAGE for a WHEEL & AXLE

actual mechanical advantage (AMA) = Resistance = Fr Effort Fe

Torque is a twisting action. The units for torque in the metric system are Newton-meters (ft-lbs or inch-lbs are typical units in the english system). The torque associated with a force is equal to the product of the force and the perpendicular distance to the center of rotation. For a wheel and axle, this distance is equal to the radius at which the force is applied. Thus: 휏 = 퐹 ∙ 푟

Rotary Motion is the circular motion which occurs when the wheel and axle are rotated about the centerline axis. Rotary motion is typically specified in terms of angular position (in degrees) or rotational speed (in revolutions per minute [rpm]).

Linear Motion is the straight-line motion which occurs when a wheel rolls along a flat surface. The linear distance traveled when the wheel completes one revolution is equal to the circumference of the wheel. Thus: 퐶 = 휋푑 = 2휋푟

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 Wheel & Axle Example Documentation: Perform the following: • Sketch the wheel and axle • Label the effort (on the wheel in this case) and the resistance (on the axle in this case) • Measure and label quantities necessary to determine the ideal mechanical advantage • Calculate the ideal mechanical advantage • Measure the effort associated with rotating the wheel to slowly lift 9.8N at the axle • Measure the distances moved by the effort and the resistance as the 9.8N is lifted 20.0 cm • Calculate the actual mechanical advantage • Calculate the work input, the actual work output, and the efficiency

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Incline Plane – a flat sloping surface along which an object can be pushed or pulled. The advantage of the incline plane is that it reduces the effort that is required to raise an object from a lower to a higher level. The trade-off comes from the fact that the effort must be applied over a greater distance than the object is lifted Fe vertically. The Resistance is equal to the weight of the object being lifted.

Fr MECHANICAL ADVANTAGE: 1. IDEAL MECHANICAL ADVANTAGE for an INCLINED PLANE

ideal mechanical advantage (IMA) = Length along the ramp the object is pushed = L Height the object is lifted H

The IMA can also be written using Right TriangleTrigonometry!

IMA = 1 SIN(θ)

2. ACTUAL MECHANICAL ADVANTAGE for an INCLINED PLANE

actual mechanical advantage (AMA) = Resistance = Fr Effort Fe

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 Incline Plane Example Documentation: Perform the following: • Sketch the inclined plane • Label the effort and the resistance • Measure and label quantities necessary to determine the ideal mechanical advantage • Calculate the ideal mechanical advantage • Measure the angle of the inclined plane • Calculate the ideal mechanical advantage using the angle of the inclined plane • Measure the resistance (note … it is the weight of the object being moved up the plane) • Measure the effort required to slowly move the object up the inclined plane • Calculate the actual mechanical advantage • Calculate the work input, the actual work output, and the efficiency

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Wedge - Wedges are used to separate or hold devices. There are two major differences between inclined planes and wedges. During its use, an inclined plane remains stationary, while the wedge moves. With an inclined plane the effort force is applied parallel to the slope of the incline. With a wedge the effort force is applied to the vertical edge (height) incline. Fe

L Fr Fr

MECHANICAL ADVANTAGE: 1. IDEAL MECHANICAL ADVANTAGE for a WEDGE

ideal mechanical advantage (IMA) = Length = L thickness t

2. ACTUAL MECHANICAL ADVANTAGE for a WEDGE

actual mechanical advantage (AMA) = Resistance = Fr Effort Fe

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 Wedge Example Documentation: Perform the following: • Sketch the wedge • Label the effort and the resistance • Measure and label quantities necessary to determine the ideal mechanical advantage • Calculate the ideal mechanical advantage

Date Completed: Preliminary Final Grader Name: Initials: Grade: Grade: Initials:

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Screw - a combination of two other simple machines: 1) an inclined plane (wrapped around a cylinder) 2) a wheel and axle

The screw may be used to change from rotary to straight line (linear) motion.

Screw Pitch is the distance between two adjacent threads on a screw. The formula to calculate pitch:

Pitch = 1 Number of threads per inch of length

The Circumference of the screw is calculated using the Geometry formula: 퐶 = 휋푑 = 2휋푟

MECHANICAL ADVANTAGE:

1. IDEAL MECHANICAL ADVANTAGE for a SCREW

ideal mechanical advantage (IMA) = Circumference Pitch

One convenient method for explaining why the IMA is calculated using this formula is through the use of the concept that the Work Input during one revolution of the Effort (at the end of the lever) is equal to the Ideal Work Output as the Resistance is raised (on top of the screw)

one revolution of the effort => resistance is lifted a height equal to the p pitch

Work Input = Ideal Work Output => Fe * Circumference = Frideal * Pitch

=> IMA = Frideal = Circumference Fe Pitch

Note: This conceptual approach is appropriate for all compound machines.

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2. ACTUAL MECHANICAL ADVANTAGE for a SCREW

actual mechanical advantage (AMA) = Resistance = Fr Effort Fe

 Screw Example Documentation: Perform the following • Sketch the screw • Label the effort and the resistance • Measure and label quantities necessary to determine the ideal mechanical advantage • Calculate the ideal mechanical advantage

Date Completed: Preliminary Final Grader Name: Initials: Grade: Grade: Initials:

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 Contemporary Examples of Simple Machines Find 10 contemporary examples of simple machines that you encounter in your everyday life. Sketch them, make appropriate measurements, and calculate their ideal mechanical advantages.

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SIMPLE MACHINES - IMPORTANT CONCEPT RECAP:

Work – Work is the amount of energy that is transmitted to or removed from an object by the action of a force through a distance. Work is only done if there is motion! [UNITS: Newton-Meter = Joules]

Power – Power is the rate of work with respect to time. [UNITS: Joules/Second = Watts]

Energy – A measure of the ability of an object to effect change in itself or the environment. It is a measure of the capacity for doing work. [UNITS: Newton-Meter = Joules]

Conservation of Energy – Energy can neither be created nor destroyed, only altered in form

Efficiency – A measure of how close to “perfect” something is. An ideal device is 100% efficient, with no losses of any kind. Actual devices are always less than 100% efficient, due to losses inherent in their use (like friction)

Torque– Torque is a measure of the twisting action of a force. It is equal to the product of the force and the perpendicular distance to the pivot point/fulcrum. Torque can exist even without motion! [UNITS: Newton-Meter]

Torque = Force x perpendicular distance to the pivot point

SIMPLE MACHINE SUMMARY:

Purpose of Simple Machines – To transmit energy through a system by manipulating force, speed, and direction

Mechanical Advantage – A ratio that measures the degree to which a simple machine makes a job easier

• Ideal Mechanical Advantage (IMA) – The mechanical advantage for a machine when all of the work input from the effort is converted into a useful work output. The IMA can be found using equations that are unique for each type of simple machine (see earlier pages … especially pg4): L R lever: IMA = e Pulley: IMA = N Wheel and Axle: IMA = Lr r L L 2πR Inclined Plane: IMA = Wedge: IMA = Screw: IMA = H t p

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• Actual Mechanical Advantage (AMA) – The mechanical advantage for a machine when it is in use. The AMA takes into account that not all of the work input from the effort can be converted into useful work output. The AMA is always equal to the ratio of the resistance and the effort:

Resistance F AMA = = r Effort Fe

Work and Power:

• Work and Power Input – The work input is equal to the product of the effort and the distance moved, in the direction of the effort. The power is equal to the rate of doing work with respect to time:

F D Work Input = F D Power Input = e e e e t

• Ideal Work and Power Output – The Ideal Work Output is equal to the Work Input. The Ideal Power Output is equal to the Power Input. An Ideal Simple Machine is 100% efficient.

• Actual Work and Power Output – The Actual Work Output is less than the Work Input. The Actual Power Output is less than the Power Input. All Actual Simple Machine are less than 100% efficient.

F D Actual Work Output = F D Power Output = r r Actual Efficiency < 100% r r t

Efficiency – The efficiency of a machine (in %) is equal to 100 times the ratio of the Actual Mechanical Advantage (AMA) to the Ideal Mechanical Advantage (IMA). It is also equal to the actual work output divided by the work input:

Efficiency AMA Actual Work Output F D = = = r r 100 IMA Work Input FeDe

An Ideal machine would be 100% efficient, with the ideal work output being equal to the work input:

Ideal Machine => 퐼푑푒푎푙 푊표푟푘 푂푢푡푝푢푡 = 푊표푟푘 퐼푛푝푢푡 => FridealDr = FeDe Fr D => 퐼푀퐴 = ideal = e Fe Dr

ONE FINAL … AND VERY USEFUL … THING! - The equation below provides a very effective method for determining the Ideal Mechanical Advantage for every machine, regardless of whether it is simple or complex. It indicates that the Ideal Mechanical Advantage for a machine is given by the ratio of the distance moved by the effort to the distance moved by the resistance. It is an extremely useful tool:

D Distance moved by effort, in direction of effort IMA = e = Dr Distance moved by resistance, in direction opposite resistance

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 Complex Machine Example • Build a complex machine from at least two of the simple machines documented earlier • Create a sketch of the complex machine, labeling all appropriate forces, lengths, and distances • Calculate the ideal mechanical advantage by multiplying the ideal mechanical advantages for the individual simple machines that have been incorporated • Calculate the ideal mechanical advantage using the aforementioned equation D Distance moved by effort, in direction of effort IMA = e = Dr Distance moved by resistance, in direction opposite resistance

• Measure the effort and resistance • Calculate the actual mechanical advantage, work input, actual work output, and efficiency

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B: Gears

Background: • Gears are mechanisms that are used to transfer energy, rotary motion, and torque through interlocking teeth. • A gear train is made when two or more gears are meshed together. • Driver Gear - Name given to the gear which provides the source of energy input. • Driven Gear – Name given to the gear which provides the energy output. • Idler – Intermediate gear that transfers energy and motion from the Driver Gear to the Driven Gear. • When two gears mesh, the rotational speed (rpm) of the larger gear is always smaller than the rotational speed (rpm) of the smaller gear. • Gears locked together on the same shaft will always rotate in the same direction and have the same rotational speed (rpm). Gear Ratio: The Gear Ratio for a gear train is analogous to the Ideal Mechanical Advantage for a simple or compound machine. However, instead of the gear ratio representing the multiplier of force, it represents the multiplier for the torque. When two gears are meshed, the torque of the larger gear will always be larger than the torque on the smaller gear. A gear ratio that exceeds one indicates that a smaller gear is driving a larger gear.

τ N D ω GR = Gear Ratio = out = out = out = in τin Nin Din ωout

τ = Torque N = Number of Teeth D = Diameter ω = Rotational Speed (rpm) in => Driver Gear out => Driven Gear)

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Problem#1 - Two Gears: Consider the situation illustrated to the right, where a small counterclockwise rotating driver gear (Nin = 6, Din = 2.0 cm, ωin = 40 rpm) is causing a larger driven gear (Nout = 12, Dout = 4.0 cm, ωout = 20 rpm) to rotate clockwise.

Respond to the following prompts:

 The gear ratio can be found three ways using the given information. Show that all three methods agree that the gear ratio is 2.0

 Newton’s Third Law is generally stated as “For every action there is an equal and opposite reaction”. In terms that are helpful for this problem … “If the driver gear exerts a force on the driven gear, then the driven gear exerts a force on the driver gear that is equal in magnitude and opposite in direction”. Suppose the driver gear exerts a force of 5.0 Newtons on the driven gear, in the downward direction at their point of contact. o Calculate the torque that the contact force between the two gears exerts on the driven gear and indicate its direction (CCW or CW)

o Calculate the torque that the contact force between the two gears exerts on the driver gear and indicate its direction (CCW or CW)

o Calculate the gear ratio using the torques and show that this new method agrees with the other three methods from above

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Problem#2 – Simple Gear Train Consider the gear train below, where the driver gear (A) is spinning clockwise at a rotational speed of 60 rpm as the result of an input torque of 100 Nm.

Respond to the following prompts:  What is the gear ratio between A and B? B and C? C and D?

 What is the total gear ratio for the entire gear train? (Note: for a simple gear train, the gear ratio for the entire gear train is equal to the product of the individual gear ratios.)

 What are the rotational speeds for B, C, and D?

 What are the magnitude and direction of the output torque for D?

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Problem#3 – Compound Gear Train IMPORTANT NOTE: Gears that are on the Consider the gear train below, where the driver gear (A) is spinning clockwise same shaft (like GEAR B at a rotational speed of 40 rpm as the result of an input torque of 30 Nm. and GEAR C here) combine for a gear ratio GEAR A equal to 1. This occurs GEAR C because the torque input is equal to the torque output. In other words, GEAR D gears on the same shaft do not multiply the GEAR B torque.

Respond to the following prompts:  Count the number of teeth on each of the gears:

 What is the gear ratio between A and B? B and C? C and D?

 What is the total gear ratio for the entire gear train?

 What is the rotational speed of gear D?

 What are the magnitude and direction of the output torque for D?

Date Completed: Preliminary Final Grader Name: Initials: Grade: Grade: Initials:

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Application#1 – Self-Directed with Gear Ratio > 1

 Use the plastic gears provided to create a gear train with at least three gears and a gear ratio greater than one, and complete the following steps:

o Sketch the gear train

o Calculate the gear ratio

o Qualitatively compare the rotational speeds for the driver gear and the driven gear by spinning the driver gear observing whether the rotational speed (rpm) of the driven gear is less than, greater than, or equal to the rotational speed for the driver gear.

o Qualitatively compare the torques for the driver gear and the driven gear by grabing hold of the driver gear and the driven gear like two knobs and observe whether the torque for the driver is less than, greater than, or equal to the torque for the driven gear.

Date Completed: Preliminary Final Grader Name: Initials: Grade: Grade: Initials:

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Application#2 – Self-Directed with Gear Ratio < 1

 Use the plastic gears provided to create a gear train with at least three gears and a gear ratio smaller than one, and complete the following steps:

o Sketch the gear train

o Calculate the gear ratio

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Design Project – SAE International – A World in Motion II

 The Society of Automotive Engineers, Inc. has created kits that facilitate learning about gear trains. One of these kits, A World in Motion II – The Design Experience – Student Design Team, comes with the following components:

o 1 vehicle frame o 4 15-tooth gears (1.5 cm diameter) o 4 45-tooth gears (4.5 cm diameter) o 2 75 tooth gears (7.5 cm diameter) o 12 drive collars o 4 gear axles o 20 axle bushings o 20 rubber spacers o 4 wheels o 2 wheel axles o 1 motor and motor mount assembly

Constraints: • The only supplies you may use are those contained within the box as issued. • One of the 15 tooth gears must be attached to the motor shaft and serve as the first gear in any gear train that is constructed. • The final gear in any gear train must be attached to the same shaft as the drive wheels. • The motor must be able to move the car along a flat surface.

FIRST PHASE – Exploring Possibilities: Your objective for this phase is to determine what arrangement of the gears will meet the following design criteria, within the above constraints a. The simple gear train with the largest gear ratio b. A simple gear train with the smallest gear ratio c. A compound gear train with the largest gear ratio

For each case, you are to: o sketch the gear train o calculate the gear ratio for each set of meshing gears o calculate the overall gear ratio for the entire gear train o determine the output torque if the input torque is 10.0 g cm o determine the output speed if the input speed is 1000.0 rpm

Case1: The simple gear train with the largest gear ratio

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Case2: A simple gear train with the smallest gear ratio

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Case3: A compound gear train with the largest gear ratio

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SECOND PHASE – Hill Climbing: Your objective for this phase is to design a gear train that will enable your vehicle to climb the steepest possible incline, within the aforementioned constraints.

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C: Pulleys & Belts and Sprockets & Chains

Background: • Pulleys & Belts and Sprockets & Chains are mechanisms that are used to transfer energy, rotary motion, and torque from one place to another (the pulleys or sprockets) through the use of a continuous and flexible connector (the belt or chain). • Driver Pulley/Sprocket - Name given to the pulley/sprocket which provides the source of energy input. • Driven Pulley/Sprocket – Name given to the pulley/sprocket which provides the energy output. • When two pulleys/sprockets are connected by a belt or chain, the rotational speed (rpm) of the larger pulley/sprocket is always smaller than the rotational speed (rpm) of the smaller pulley/sprocket. Drive Ratio: The concept of a Drive Ratio for a Pulleys & Belts or Sprockets & Chains is analogous to gear ratios for gear trains. A drive ratio that exceeds one indicates that a smaller pulley/sprocket is driving a larger pulley/sprocket. τ D ω DR = Drive Ratio = out = out = in τin Din ωout (Notes: τ = Torque, D = Diameter, ω = Rotational Speed (rpm), in => Driver Gear, out => Driven Gear)

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EP@BHS-TOPIC 2: Energy, UNIT2.6: Mechanisms Page 32

Problem#1 – Belt Drive System: Consider the situation illustrated below, where a small clockwise rotating pulley is being used to drive a larger clockwise rotating pulley.

 Calculate the drive ratio two ways:

 Determine the required input torque if the required output torque is 55 ft-lb:

Problem#2 – Chain Drive System: Consider the situation illustrated below, where a small clockwise rotating sprocket is being used to drive a larger clockwise rotating sprocket.

 Calculate the drive ratio two ways:

 Determine the required input rotational speed if the required output rotational speed is 45 rpm:

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EP@BHS-TOPIC 2: Energy, UNIT2.6: Mechanisms Page 33

Topic 1.1 Culminating Example: Mr. Wawrzyniak’s Univega Maxima Sport!

Mr. Wawrzyniak has brought in an old bicycle for us to use to illustrate examples of various machines.

 Your first objective is to determine the gearing that Mr. Wawrzyniak should use to climb the steepest hill. Include a sketch that illustrates important details regarding dimensions and configuration as well as the overall drive ratio and the overall mechanical advantage.

 Your second objective is to determine the gearing that Mr. Wawrzyniak should use to achieve maximum speed. Include a sketch that illustrates important details regarding dimensions and configuration as well as the overall drive ratio and the overall mechanical advantage.

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EP@BHS-TOPIC 2: Energy, UNIT2.6: Mechanisms Page 34

 Your third objective is to find two applications of compound machines on the bicycle. Include sketches that illustrate important details regarding dimensions and configuration as well as the overall mechanical advantage for each application (include additional pages as necessary):

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EP@BHS-TOPIC 2: Energy, UNIT2.6: Mechanisms Page 35

Topic 1.1 Key Term Crossword

1 2 3

4 5

6 7

8 9

10 11 12

15 16 17

20 21

24 25 26

www.CrosswordWeaver.com

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EP@BHS-TOPIC 2: Energy, UNIT2.6: Mechanisms Page 36

ACROSS DOWN

5 An external force applied to an object. 1 Creating, designing, and transmitting technical 6 A circular toothed object used to transfer information so that people can understand it rotary motion and torque through interlocking easily and use it safely, effectively, and teeth. efficiently. 8 A rigid bar used to exert a pressure or sustain 2 The ratio of useful energy output to the total a weight at one point of its length by the energy input, or the percentage of the work application of a force at a second and turning input that is converted to work output. at a third on a fulcrum. 3 A force that produces or tends to produce 11 Distance between adjacent threads in a screw. rotation or torsion. 13 A series of usually metal links or rings 4 Two different sized circular objects that are connected to or fitted into one another and attached together and turn as one. used to transmit motion and power within a 7 The fixed point around which a lever rotates. sprocket system. 9 A flat surface set at an angle or an incline with 14 A profession for which one trains and which is no moving parts that is able to lift objects by undertaken as a permanent calling. pushing or pulling the load. 17 A substance that tapers to a thin edge and is 10 The resistance that one surface or object used for splitting, raising heavy bodies, or for encounters when moving over another. tightening by being driven into something. 12 A gear positioned between the driver and the 18 Impeding effect exerted by one material object driven gear used to change rotational on another. direction. 20 A toothed wheel whose teeth engage the links 15 Any of various elementary mechanisms of a chain. including the lever, the wheel and axle, the 22 The ratio of the magnitude of the resistance pulley, the inclined plane, the wedge, and the and effort forces applied a system. screw. 23 The structure of or the relationship of the parts 16 An inclined plane wrapped around a cylinder, in a machine, or in a construction or process forming the path and pitch. comparable to a machine. 19 The turning effect of a force about a point 24 A condition where there are no net external equal to the magnitude of the force times the forces acting upon a particle or rigid body and perpendicular distance from the point to the the body remains at rest or continues at a line of action from the force. constant velocity. 21 A type of lever that is a wheel with a groove in 27 Ratio of distance traveled by the applied effort its rim, which is used to change the direction and resistance force within a system. or multiply a force exerted by a rope or cable. 25 A continuous band of tough flexible material used to transmit motion and power within a pulley system. 26 The recognized accreditor for college and university programs in applied science, computing, engineering, and technology.

Help with some of the more obscure entries in Topic 1.1 Key Term Crossword: 1-Down: TechnicalCommunication 18-Across: ResistanceForce 23-Across: Mechanism 24-Across: StaticEquilibrium

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