Advances in Science and Technology Received: 2019.10.15 Revised: 2020.01.10 Research Journal Accepted: 2020.02.01 Volume 14, Issue 1, March 2020, pages 50–57 Available online: 2020.02.14 https://doi.org/10.12913/22998624/113286

Proposal of a Mechanism for Movement

Vladimír Pavelčík1*, Dalibor Barta1, Milan Sapieta1

1 University of Žilina, Faculty of Mechanical Engineering, Univerzitna 1, 010 26, Žilina, Slovak Republic * Corresponding author’s e-mail: [email protected]

ABSTRACT This article is focused on the height adjustment of a front car seat. The goal was to design seat movement in pure vertical direction. The article begins with a theoretical introduction, in which the functions and parts of car seats were described. The next part contains possible schematic designs of a mechanism, as well as the reasons for pos- sible changes of the contemporary mechanisms. Afterwards, some functional parameters of the chosen schemat- ically-designed mechanism were calculated, the results could then be used for further calculations needed for the creation of a three-dimensional model of the mechanism. The article deals mainly with the theoretical principles, and there are many further possibilities for development within the subject.

Keywords: car seat, height adjustment, design of kinematics, schematic design.

INTRODUCTION FUNCTIONS AND PARTS OF A CAR SEAT

Nowadays, it is almost impossible to imagine Because people differ from each other in their a means of transport aimed at transporting people body-sizes, shapes, weight, etc., and this differ- without seats. Automobiles are not an exception. ence is worldwide territorial, a seat has to hold a People are different from numerous points of view, person sitting in the correct position, due to the taking into account their statures, or preferences safety and health protection reasons (correct posi- of positions they consider comfortable. Regarding tioning of the back, shoulders, hips, legs, support- the impossibility to manufacture a seat adjusted to ing correct angles between different parts of the everybody, a principle of seat adjustment accord- body, etc.). An incorrect position of the seat also ing to the needs of a seated person is being used. influences concentration and level of tiredness Various seat adjustment mechanisms are used. of the driver and other psychological aspects of Seats can be divided into more categories accord- safety in the road transportation [9, 11]. Another ing to the number of their mechanisms and origin important function is to give the driver the best of power for modifying their position. The divi- possible view on the road in front of the car as sion reflects also price of a vehicle; consequently, well as rear-view mirrors. low- and middle-class-vehicles contain seats with A cushion and a central part of a seat back are fewer mechanisms, while more luxurious vehicles used to hold the passenger in a correct position, have seats which are adjusted in a more complex as well as provide him with the basic comfort and way. As in other industrial areas, the automotive protection. Side cushions protect the passenger industry involves innovations as essential part of from unwanted motion caused by the centrifugal evolution, including the adjustment mechanisms force in road curves. They also contribute by their of car seats. The task of the article was to attempt part to the comfort. A side cushion might contain one of such innovations – to design a principle of an air-bag. After an accident, when the air-bag de- operation of a mechanism reflecting an innovative ployed, it is highly recommended to replace the approach to seat adjustment. whole seat.

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A headrest is one of the most important pas- rotating the sheets of the frame. According to sive safety elements. Equally to the cushion and the number of possible movements, car seats are backrest, it can be adjustable (in this case it is a divided to: 2-way, 4-way, 6-way and more-way. separate part of a car seat and it can be removed The possible movements of a six-way car seat are with no difficulties) or it may not be adjustable, presented in Figure 2. and then it is not removable. In contrast, an arm- Plastic parts mostly correspond to different rest, which is not in the figure, is only an element coverings. Some functional elements, such as the of comfort. Moreover, it does not necessarily lever of the height adjustment mechanism, can be have to be a part of the seat, it can constitute a also made of plastic materials. A plastic table for part of the central console. There are many more a rear seat passenger may sometimes be attached possible elements to be added, for example a seat on the back side of the some row seats. Other- belt mechanism, parts of seat adjustment mecha- than-fixed connections between metal parts are nisms, a trim-based pocket, where small things usually made of plastic to avoid noise contamina- can be stored by a rear-seat passenger, etc. tion when adjusting a seat to the correct position From the inner point of view, parts of a car [14]. Foam parts are considered to be a very im- seat can be divided into: portant comfort element. They are usually made •• metal parts, of polyurethane, in which some additives can be •• plastic parts, inserted and are mostly connected with the metal •• foam parts, dampening elements [7]. The foam can be found •• trims, in the cushion, backrest and headrest. Trims are •• other parts. the most important part for the first impression of a customer, who see them, touch them, and who The group of metal parts consists of: should feel comfortable with them. Their mate- •• basic frame, rial can be very variable – leather, textile, plastic •• mechanisms, •• dampening elements, fibres etc [1]. •• others. The basic frame means various welded sheets, DEFINED POINTS OF A CAR SEAT which hold the passenger in the correct position, which is essential from the medical point of view, The development of a new car seat begins and secure the proper shape of the seat. The metal after receving the order from a customer. The mechanisms are the parts used to adjust the ba- customer specifies (not only) positions of various sic frame to the required position by moving and points and fields, which the developer has to take

Fig. 2. An example of possible movements Fig. 1. Parts of a front-row car seat of a 6-way front-row car seat

51 Advances in Science and Technology Research Journal Vol. 14(1), 2020 into the account. These points mostly have to se- possible innovative H-point field taking into ac- cure the person’s safety and also ensure that the count the conditions mentioned above is present- car is being driven safely by the driver. During ed in Figure 4. crash-tests of a vehicle, the risk is too high to let It is wise to design a mechanism (at least any person sit on the seat, so dummies are usually schematically), which is able to provide such an used instead. Only some of the points and fields H-point field. On the basis of Figure 4, the hand- are mentioned here, because the number of them powered lift shall lie in a purely vertical direc- is fairly high. For example, the field of points tion. For the purposes of this innovation process, representing the driver’s view, which creates an at least a few variants had to be presented. Ac- eye-ellipse securing good view not only out of the cording to this information, some parallels can be vehicle, but in the interior of the vehicle as well, seen in the technical solutions all over the world. which is important from the safety point of view. Exactly this kind of movement can be noticed in A point, which represents the centre of rotation of combustion engines (crank shaft – connecting the head (cervical vertebrae); Heel point, which rod – piston), from other examples can be men- represents the contact of the driver’s heel with the tioned, including cam mechanism, pantographic floor of the vehicle; and perpendicular projection mechanism or hydraulic or pneumatic pistons of the axis of rotation of the thighs to the torso of performing the wanted movement [2, 3, 8, 5]. The the body to the xz plane, which is called H-point simplest way would be the hydraulic one. (Hip – point), sometimes reffered to as SRP – Seat Two principles of hydraulic mechanisms can reference point. The set of all H-points available be used. As a Variant A it is the hydraulic mecha- on a car seat is called H-point field (Fig. 3). nism with single acting cylinders (Fig. 5), where The whole innovation process starts with a hand-powered oil pump increases the pressure in reasoning about the height adjustment. Statis- tics state that the tallest people set their seat to the pistons and cause the movement up, while the the position B (Fig. 3), because of their need manually operated valve in cooperation with per- to have sufficient space for their legs as well as son’s gravity causes the movement down. Vari- for their heads. In contrast, the shortest people ant B presents the mechanism with double acting would, generally, use the position D in the pic- cylinders (Fig. 6), which is based on the principle ture (Fig. 3). Short people usually have shorter of pumping the liquid from one piston to other legs, but they still need to remain in contact with pedals. Additionally, short people still need to see the road above the . An aver- age person would adjust the seat somewhere in between those positions, but points A and C stay unused. The task is to design H-point field, which would remove the points A and C and widen the H-point field in the area near points B and D. One

Fig. 3. H-point field

Fig. 5. Variant A – Hydraulic principle Fig. 4. Innovated H-point field – single acting cylinders

52 Advances in Science and Technology Research Journal Vol. 14(1), 2020

selected. Unlike in the engine, the piston can- not be the part causing the movement of the whole mechanism, because the piston must be somehow connected to the person to ensure his or her lift. The first idea resulted in vari- ant C, which uses group of gear wheels and gear racks (Fig. 7), where the gear wheel driv- en through a mechanism by hand would cause the movement of the gear rack connected via binary element to both “crank shaft” and “con- Fig. 6. Variant B – Hydraulic principle – necting rod”. double acting cylinders – pumping However, this solution would significantly increase the total mass of the seat, so a slightly pistons (amount and dimensions of the pistons modified mechanism can be seen on the scheme must be calculated). of the variant D at the bottom (Fig. 8). Here, the The advantages of hydraulics could be low crank mechanism as well as the binary element force needed to power the mechanism, exact po- remain, but the group of gears is replaced by one sitioning; moreover, with the use of more pis- threaded rod and two moving nuts. The threaded tons, the dimensions decrease as well. However, rod must have two threaded parts and threads there are two important disadvantages of using must be oriented oppositely. Then, the rotation of hydraulics. Firstly, the weight, which is caused the threaded rod causes lift of the cushion via the by hydraulic liquid as well as mass of hydraulic binary element and crank mechanism. sysem components and which is very important parameter related for example to fuel consump- tion and emisions, or to the braking character- istics of a vehicle [10, 6]. Secondly, no liquid CALCULATION OF BASIC should be flowing out of any car seat in case of, DIMENSIONS OF THE CRANK for example an accident, which could not be en- PAR=T OF THE MECHANISM sured without many difficulties. As a result, the hydraulic mechanism cannot be easily used for On the basis of the variant D (Fig. 8), a scheme height adjustment of a car seat. containing symbols (Fig. 9) is derived. In order to advance the proposal to the next Afterwards, the following equations can be level, a principle of crank mechanism had been written:

R: (1)

! 𝑭𝑭𝒊𝒊𝒊𝒊 = 𝟎𝟎; 𝑹𝑹𝒚𝒚 + 𝑵𝑵𝒍𝒍 · 𝒔𝒔𝒔𝒔𝒔𝒔(𝜷𝜷) = 𝟎𝟎; (2) 𝒈𝒈 𝒍𝒍 H: ! 𝑭𝑭𝒊𝒊𝒊𝒊 = 𝟎𝟎; −𝑭𝑭 − 𝑻𝑻 − 𝑵𝑵 · 𝒄𝒄𝒄𝒄𝒄𝒄(𝜷𝜷) = 𝟎𝟎; (3) ! 𝑭𝑭𝒊𝒊𝒊𝒊 = 𝟎𝟎; −𝑵𝑵𝒍𝒍 · 𝒔𝒔𝒔𝒔𝒔𝒔(𝜷𝜷) − 𝑵𝑵𝒓𝒓 · 𝒔𝒔𝒔𝒔𝒔𝒔(𝜶𝜶) + 𝑵𝑵𝒒𝒒 · 𝒄𝒄𝒄𝒄𝒄𝒄(𝜸𝜸) = 𝟎𝟎 ; (4)

L: ! 𝑭𝑭𝒊𝒊𝒊𝒊 = 𝟎𝟎; 𝑵𝑵𝒍𝒍 · 𝒄𝒄𝒄𝒄𝒄𝒄(𝜷𝜷) − 𝑵𝑵𝒓𝒓 · 𝒄𝒄𝒄𝒄𝒄𝒄(𝜶𝜶) − 𝑵𝑵𝒒𝒒 · 𝒔𝒔 𝒔𝒔𝒔𝒔(𝜸𝜸) = 𝟎𝟎; (5)

! 𝑭𝑭𝒊𝒊𝒊𝒊 = 𝟎𝟎; 𝑳𝑳𝒚𝒚 + 𝑵𝑵𝒓𝒓 · 𝒔𝒔𝒔𝒔𝒔𝒔(𝜶𝜶) = 𝟎𝟎; (6)

S: ! 𝑭𝑭𝒊𝒊𝒊𝒊 = 𝟎𝟎; 𝑳𝑳𝒛𝒛 + 𝑵𝑵𝒓𝒓 · 𝒄𝒄𝒄𝒄𝒄𝒄(𝜶𝜶) = 𝟎𝟎; (7)

! 𝑭𝑭𝒊𝒊𝒊𝒊 = 𝟎𝟎; −𝑵𝑵𝒒𝒒 · 𝒄𝒄𝒄𝒄𝒄𝒄(𝜸𝜸) − 𝑭𝑭𝑸𝑸 = 𝟎𝟎 ; (8)

! 𝑭𝑭𝒊𝒊𝒊𝒊 = 𝟎𝟎; 𝑵𝑵𝒒𝒒 · 𝒔𝒔𝒔𝒔𝒔𝒔(𝜸𝜸) + 𝑺𝑺𝒛𝒛 = 𝟎𝟎; where Nr, Nq and Nl [N] are axial forces, Fg, FQ [N], , , [°] are parameters given R , L , L , S [N] are reactions of the frame, in Fig. 9. Natually, friction can influence y y z z α β γ the final result, so the friction caused by

53 Advances in Science and Technology Research Journal Vol. 14(1), 2020

Fig. 7. Variant C – mechanism with gear racks and gear wheels

Fig. 8. Variant D – mechanism with the threaded rod Fig. 9. Angles and lengths of the crank part of the mechanism normal force Ry is introduced in equation (2) as force T [N]. This force is equal to:

(9) minimum of FQ function. Some mathematical op- erations are needed in a few steps to derive FQ where𝑻𝑻 = 𝑹𝑹f [-]𝒚𝒚 · 𝒇𝒇is =coefficient−𝑵𝑵𝒍𝒍 · 𝒔𝒔𝒔𝒔𝒔𝒔 (of𝜷𝜷 )friction· 𝒇𝒇; at point R as a function of lengths of parts r, l, h, q of the (Fig. 9). In order to minimize the torque needed multibody system (Fig. 9). Below, only some of to push the cushion up, it is essential to find the the steps are stated:

−𝑵𝑵𝒍𝒍 · 𝒔𝒔𝒔𝒔𝒔𝒔(𝜷𝜷) − 𝑵𝑵𝒓𝒓 · 𝒔𝒔𝒔𝒔𝒔𝒔(𝜶𝜶) + 𝑵𝑵𝒒𝒒 · 𝒄𝒄𝒄𝒄𝒄𝒄(𝜸𝜸) = 𝟎𝟎; /: (−𝒔𝒔𝒔𝒔𝒔𝒔 𝜶𝜶) 𝑵𝑵𝒍𝒍 · 𝒄𝒄𝒄𝒄𝒄𝒄(𝜷𝜷) − 𝑵𝑵𝒓𝒓 · 𝒄𝒄𝒄𝒄𝒄𝒄(𝜶𝜶) − 𝑵𝑵𝒒𝒒 · 𝒔𝒔𝒔𝒔𝒔𝒔(𝜸𝜸) = 𝟎𝟎; /: (𝐜𝐜𝐜𝐜𝐜𝐜 𝜶𝜶)

𝑠𝑠𝑠𝑠𝑠𝑠(𝛽𝛽) 𝑐𝑐𝑐𝑐𝑐𝑐(𝛽𝛽) 𝑐𝑐𝑐𝑐𝑐𝑐(𝛾𝛾) 𝑠𝑠𝑠𝑠𝑠𝑠(𝛾𝛾) 𝑁𝑁" · $ + / − 𝑁𝑁1 · $ + / = 0; 𝑠𝑠𝑠𝑠𝑠𝑠(𝛼𝛼) 𝑐𝑐𝑐𝑐𝑐𝑐(𝛼𝛼) 𝑠𝑠𝑠𝑠𝑠𝑠(𝛼𝛼) 𝑐𝑐𝑐𝑐𝑐𝑐(𝛼𝛼)

𝒔𝒔𝒔𝒔𝒔𝒔(𝜷𝜷) 𝒄𝒄𝒄𝒄𝒄𝒄(𝜷𝜷) + 𝒔𝒔𝒔𝒔𝒔𝒔(𝜶𝜶) 𝒄𝒄𝒄𝒄𝒄𝒄(𝜶𝜶) 𝑵𝑵𝒒𝒒 = 𝑵𝑵𝒍𝒍 · ; 𝒄𝒄𝒄𝒄𝒄𝒄(𝜸𝜸) 𝒔𝒔𝒔𝒔𝒔𝒔(𝜸𝜸) + 𝒔𝒔𝒔𝒔𝒔𝒔(𝜶𝜶) 𝒄𝒄𝒄𝒄𝒄𝒄(𝜶𝜶) 𝒔𝒔𝒔𝒔𝒔𝒔(𝜷𝜷) 𝒄𝒄𝒄𝒄𝒄𝒄(𝜷𝜷) 𝒈𝒈 + −𝑭𝑭 𝒔𝒔𝒔𝒔𝒔𝒔(𝜶𝜶) 𝒄𝒄𝒄𝒄𝒄𝒄(𝜶𝜶) 𝑵𝑵𝒒𝒒 = · ; 𝒄𝒄𝒄𝒄𝒄𝒄(𝜷𝜷) − 𝒇𝒇 · 𝒔𝒔𝒔𝒔𝒔𝒔(𝜷𝜷) 𝒄𝒄𝒄𝒄𝒄𝒄(𝜸𝜸) 𝒔𝒔𝒔𝒔𝒔𝒔(𝜸𝜸) + 𝒔𝒔𝒔𝒔𝒔𝒔(𝜶𝜶) 𝒄𝒄𝒄𝒄𝒄𝒄(𝜶𝜶)

𝒔𝒔𝒔𝒔𝒔𝒔(𝜷𝜷) 𝒄𝒄𝒄𝒄𝒄𝒄(𝜷𝜷) + 𝒄𝒄𝒄𝒄𝒄𝒄(𝜸𝜸) 𝒔𝒔𝒔𝒔𝒔𝒔(𝜶𝜶) 𝒄𝒄𝒄𝒄𝒄𝒄(𝜶𝜶) 𝑭𝑭𝑸𝑸 = 𝑭𝑭𝒈𝒈 · · ; 𝒄𝒄𝒄𝒄𝒄𝒄(𝜷𝜷) − 𝒇𝒇 · 𝒔𝒔𝒔𝒔𝒔𝒔(𝜷𝜷) 𝒄𝒄𝒄𝒄𝒄𝒄(𝜸𝜸) 𝒔𝒔𝒔𝒔𝒔𝒔(𝜸𝜸) + 𝒔𝒔𝒔𝒔𝒔𝒔(𝜶𝜶) 𝒄𝒄𝒄𝒄𝒄𝒄(𝜶𝜶) 54 Advances in Science and Technology Research Journal Vol. 14(1), 2020

(10)

𝑸𝑸 𝒈𝒈 𝒔𝒔𝒔𝒔𝒔𝒔(𝜶𝜶 + 𝜷𝜷) · 𝒄𝒄𝒄𝒄𝒄𝒄(𝜸𝜸) In order to find𝑭𝑭 FQ= as𝑭𝑭 a function· of parts dimensions, the following. three cosine-rule equations must be added: 𝐜𝐜𝐜𝐜𝐜𝐜(𝜶𝜶 − 𝜸𝜸) · (𝐜𝐜𝐜𝐜𝐜𝐜(𝜷𝜷) − 𝒇𝒇 · 𝐬𝐬𝐬𝐬𝐬𝐬(𝜷𝜷)) (11) 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝒓𝒓 + 𝒉𝒉 − 𝒍𝒍 𝜶𝜶 = 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 ; 𝟐𝟐 · 𝒓𝒓 · 𝒉𝒉 (12) 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝒉𝒉 + 𝒍𝒍 − 𝒓𝒓 𝜷𝜷 = 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 ; 𝟐𝟐 · 𝒍𝒍 · 𝒉𝒉 𝟐𝟐 𝟐𝟐 𝟐𝟐 (13) 𝒓𝒓 · 𝒔𝒔𝒔𝒔𝒔𝒔(𝟗𝟗𝟗𝟗 − 𝜶𝜶) 𝒓𝒓 · 𝒄𝒄𝒄𝒄𝒄𝒄(𝜶𝜶) 𝒉𝒉 + 𝒓𝒓 − 𝒍𝒍 𝜸𝜸 = 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 = 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 = 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 ; where r, l, h, q [mm] are parameters𝒒𝒒 marked in the Figure𝒒𝒒 9. The final function𝟐𝟐 · 𝒒𝒒 · 𝒉𝒉can be reached by a substitution of α (equation 10), β (11), γ (12) in equation (9):

𝐹𝐹" = ...... (14) $ 𝑟𝑟 + ℎ − 𝑙𝑙 ℎ + 𝑙𝑙 − 𝑟𝑟 ℎ + 𝑟𝑟 − 𝑙𝑙 𝐹𝐹 ∙ 𝑠𝑠𝑠𝑠𝑠𝑠 )𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 2 · 𝑟𝑟 · ℎ + 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 2 · 𝑙𝑙 · ℎ 5 · 𝑐𝑐𝑐𝑐𝑐𝑐 )𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 2 · 𝑞𝑞 · ℎ 5 = ...... 𝑟𝑟 + ℎ − 𝑙𝑙 ℎ + 𝑟𝑟 − 𝑙𝑙 ℎ + 𝑙𝑙 − 𝑟𝑟 ℎ + 𝑙𝑙 − 𝑟𝑟 Thiscos equation)𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 can2 be· 𝑟𝑟 simplified· ℎ − 𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎𝑎𝑎to: 2 · 𝑞𝑞 · ℎ 5 · ) 2 · 𝑙𝑙 · ℎ − 𝑓𝑓 · sin )𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 2 · 𝑙𝑙 · ℎ 55

(15) where k is substitution: 𝑭𝑭𝑸𝑸 = 𝑭𝑭𝒈𝒈 · 𝒌𝒌;

𝒌𝒌 = 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 (16) 𝒓𝒓 + 𝒉𝒉 − 𝒍𝒍 𝒉𝒉 + 𝒍𝒍 − 𝒓𝒓 𝒉𝒉 + 𝒓𝒓 − 𝒍𝒍 𝒔𝒔𝒔𝒔𝒔𝒔 &𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 + 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 1 · 𝒄𝒄𝒄𝒄𝒄𝒄 &𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 1 𝟐𝟐 · 𝒓𝒓 · 𝒉𝒉 𝟐𝟐 · 𝒍𝒍 · 𝒉𝒉 𝟐𝟐 · 𝒒𝒒 · 𝒉𝒉 = 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 𝟐𝟐 . 𝒓𝒓 + 𝒉𝒉 − 𝒍𝒍 𝒉𝒉 + 𝒓𝒓 − 𝒍𝒍 𝒉𝒉 + 𝒍𝒍 − 𝒓𝒓 𝒉𝒉 + 𝒍𝒍 − 𝒓𝒓 𝐜𝐜𝐜𝐜𝐜𝐜 &𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 − 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 1 & − 𝒇𝒇 · 𝐬𝐬𝐬𝐬𝐬𝐬 &𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 11 The last important𝟐𝟐 · 𝒓𝒓 ·step𝒉𝒉 is to find the 𝟐𝟐minimum· 𝒒𝒒 · 𝒉𝒉 which𝟐𝟐 · 𝒍𝒍 · 𝒉𝒉were presented schematically.𝟐𝟐 · 𝒍𝒍 · 𝒉𝒉 From those of this function of four variables r, l, h and q; ei- four schemes, the one based on the crank mecha- ther by finding the minimum of the function of nism and the threaded rod was selected for further four variables, or by reducing this function to a development. Calculation of the basic dimensions lower number of variables, or by any other math- was then taken into the point, where exact num- ematical method [12, 13]. Moreover, it is wise not bers are needed to continue with the calculation. to omit the triangle inequality, which says, that For the specific car seat, according to the techni- the sum of lengths of any two sides of triangle cal specification, some parameters are set to num- must exceed the length of the third side [4]. This bers. These are shown in the Table 1. rule has to be obeyed in the position up as well On the basis of these parameters, function as in the position down of the purposed mecha- k of four variables can be transformed to function nism. For this reason, no further calculation can of two variables r and l. The function of two vari- be made without stating the length of the lift for ables can be seen in Figure 10, where also triangle the specific car seat. inequality is shown – parts of curves lying in the

Table 1. Parameters specified for specific car seat SOLUTION RESULTS Parameter Value The article presents four variants of mecha- Lift z 40 mm nisms, which could meet the requirements for h 36 mm kinematics of the newly-designed H-point field, γ 8°

55 Advances in Science and Technology Research Journal Vol. 14(1), 2020

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