Meek. Mack. ~ Vol. 27. No. 3, pp. 235-242. 1992 0094-1 l&X/92 $5.00 + 0.00 I I ~ m l in Great BriUuL All rq~u rein'red CopyriSht C~ 1992 Perllmma Prm pig

A METHODOLOGY FOR CREATIVE MECHANISM DESIGN

HONG-SEN YAN ~ e n t of Mechanical Engineering, National Chen 8 Kung Univenity, Tainan, Taiwan 70101

(Received 25 April 1991; received for publication 29 July 1991)

Almntct--Thi$ paper summarizes the author's few.arch efforts in the creative daign of mechanism in the pat years. A da i ln methodolosy is presented for the generation of all po~ble detain concepts of mechaniams with required topological ¢haracteristica. This methodology provides a powerful tool to avoid existinlg designs which have patent protection. The rear mspeusion of off-road motmgycles is used as an example to illustrate this methodology.

INTRODUCTION

An important stage in the design of mechanisms is the conceptual phase. Designers need the ability to create new devices or to modify existing ones to achieve a desired function. This is not only the most creative part of the design process, but also the least understood.

The activity of modifying an existing design which has patent protection happens to designers most of the time. The purpose of this paper is to summarize the author's research efforts in creative mechanism design in the past years for achieving this goal.

THE DESIGN METHODOLOGY

Figure I shows a flow chart of the proposed design methodology for creative mechanism design[l-6]. This design methodology starts by investigating available existing designs to determine their topological characteristics. One of the existing designs is then selected arbitrarily to serve as the original mechanism. The second step is to transform this original mechanism into its corresponding generalized kinematic chain which has only links and revolute joints, through the process of generalization. The third step is to synthesize the atlas of kinematic chains with the required number of links and joints by number synthesis. The fourth step is to obtain specialized kinematic chains by assigning types of members and joints into elements of kinematic chains subject to design requirements through the process of respecialization. The fifth step is to identify acceptable specialized kinematic chains subject to required design constraints. The sixth step is to particularize each acceptable specialized kinematic chain into its corresponding mechanism through the process of particularization. The last step of the design methodology is to remove all existing designs from the generated atlas of mechanism to obtain new designs.

In what follows, the rear suspension of off-road motorcycles is used as an example to illustrate this design methodology.

EXISTING AND ORIGINAL MECHANISMS In general, the rear wheel suspension of a motorcycle is a four-bar linkage. However, such a

design cannot provide a large wheel travel with variable leverage ratio. Therefore, the concept of six-bar linkages is adopted for the rear suspension of off-road motorcycles, such as the Honda CR250R Pro-link (Fig. 2), the Suzuki RM250X Fuil-floater (Fig. 3), and the Kawautki KX250 Uni-trak (Fig. 4).

By studying these three existing designs, we conclude that the characteristics of their topological structures are as follows:

(!) They are planar mechanisms with one degree of freedom. (2) They consist of six members and seven joints.

235

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Fig. I. ~ d~ipn milu~tbodology.

(3) They have six revolute joints (joints a, b, c, d, e and f; R). (4) They have one prismatic joint (joint g; P). (5) They have one fixed link (member !; Gr). (6) They have a pivot arm (member 2; Li). (7) They have a swing arm (member 3; Li) in which one end is pivoted to the frame and the

other end is attached to the real wheel. (8) They have a floating link (member 4; Li). (9) They have a shock absorber consisting of a piston (member 5; Pi) and a cylinder

(member 6; Cy).

The Suzuki RM250X Full-floater (Fig. 3) is selected arbitrarily as the original mechanism. Figure $ shows a skeleton drawing of the mechanism.

The topological structure of a mechanism can best be represented by its mechanism topology matrix (MTM) [6]. The MTM of a mechanism with N links is an N x N' matrix. Diagonal element aii represents the type of member i. If member i is adjacent to member k, non-diagonal element aOc on the upper ri6ht repr"~,ents the type of joint incident to members i and k, and that on the lower left represents the name of the joint. If member i is not adjacent to member k, then aik = 0.

Fig. 2. Honda Pro-link suspension. Fig. 3. Suzuki Full-floater suspension.

A methodolol~ for creative mechaaim~ dailn 237

Fig. 4. Kawautki Uni-trak suspension.

t

I I J /

d I I /

! suwua-e~l ren iu t , J.mt.] I 6nere l lz , . g . . t l e Cll,*n ]

Fig. $. Skeleton of Suzuki ~aspemion.

For the Suzuki suspension shown in Fig. 5, its corresponding MTM is

MTM =

"Gr R R 0 0 0

a Li 0 R R 0

b 0 Li R 0 R

0 c e Li 0 0

0 d 0 0 Pi P

0 0 f 0 g Cy

GENERALIZED KINEMATIC CHAIN

The purpose of generalization is to transform the original mechanism, which involves various types of elements and joints, into a generalized kinematic chain with only links and revolute joints. The process of generalization is based on a set of generalizing rules, which are derived according to defined generalizing principles. The generalizing principles and rules are described in detail in Refs [7, 8]. Figure 6 shows a flow chart of the generalization. Through this process, we are able to study and compare different mechanisms in a very basic way. Mechanisms which at first glance appear to be different may have identical generalized forms.

For the Suzuki suspension shown in Fig. 5, the generalization is carried out as follows (Fig. 7):

(I) The fixed link (member 1) is generalized into a binary link (link I). (2) The pivot arm (member 2) is generalized into a ternary link (link 2). (3) The swing arm (member 3) is generalized into a ternary link (link 3). (4) The floating link (member 4) is generalized into a binary link (link 4). (5) The piston and cylinder of the shock absorber (members 5 and 6) are generalized into a dyad

Oinks 5 and 6). (6) The prismatic joint (g) is generalized into a revolute joint, (7) The fixed link is released.

Therefore, the selected original mechanism is transformed into a generalized kinematic chain with six links and seven revolute joints, as shown in Fig. 7.

MMT 27/3----B

238 HoNo-S~ Y ~

d(ll) ~ ) , . ,~ Table 1. The number of kinematic chains with 6-12 links F

I(Gr) 6(CU~" ~"" " 1~4tLl) 7 4 8 16 7 9 40 10

b(a) 10 230 98 14 i ! 839 189 19 12 6862 2442 354 24

fin) Fill. 6. Generalization.

ATLAS OF KINEMATIC CHAINS

This step of the design methodology is to synthesize all possible kinematic chains which have the same numbers of links and joints as the generalized kinematic chain. This is kinematic number synthesis and has been the subject of numerous studies. The term kinematic chain used here refers to a chain which is connected, closed, without any cut-link, and with simple joints only. In graph theory, it is a block [9].

A systematic and automatic approach is proposed in Ref. [10] for enumerating non- isomorphic kinematic chains based on the theory of permutation groups. As a result, the numbers of kinematic chains with up to 12 links and seven degrees of freedom are provided (Table 1). Furthermore, a computer algorithm is developed for the automatic sketching of kinematic chains [I !].

For our example, there are 2 kinematic chains with six links and seven joints, as shown in Fig. 8.

SPECIALIZED KINEMATIC CHAINS

The purpose of specialization is to assign specific types of members and joints in the available atlas of kinematic chains subject to certain design requirements.

Based on combinatorial theory, a methodology is developed in gef. [! 2] to enumerate all possible non-isomorphic specialized mechanisms for a specified kinematic chain. Also, mathematical expressions for counting the number of speciafized mechanisms are derived based on Polya's theory.

Design requirements are determined based on the topological characteristics of existing mechanisms and the designers' judgement.

For the rear suspension of off-road motorcycles, the design requirements are as follows:

(i) There must be a fixed link as the frame. (2) There must be a shock absorber. (3) There must be a swing arm to install the rear wheel. (4) The fixed link, the shock absorber and the swing arm must be distinct members.

In what follows, we list the results of a~tigning fixed link, shock absorber and swing arm to the two kinematic chains shown in Fig. 8 ac~rding to the algorithm presented in Ref. [12].

Fixed link (Gr)

For the kinematic chain shown in Fig. 8(a), the amgnment of the fixed link generates two non-isomorphic results as shown in Figs 9(a) and (b). For the kinematic chain shown in Fig. 8(b), the assignment of the fixed link Fnerates three non-isomorphic results as shown in Figs 9(c)-(e).

Shock absorber (Ss-Ss)

For the kinematic chain shown in Fig. 9(a), any one of the two dyads can be assigned as the shock absorber [Fig. 10(a)]. For kinematic chains shown in Figs 9(b)-(d), only one of the

A mmhodology for ~tivt m~hanim dmip

(a) Fig. 7. Genem/izzd kinematic chain.

(b) Fig. 8. Kinematic chains with six rinks and seven joints.

available dyadscan be assigned as the shock absorber ~Figs 10(b)-(d)]. The kinematic chain shown in Fig. 9(e) has no shock absorber available.

Swing arm (Sw)

For the kinematic chain shown in Fig. 10(a), thrcc links can be assigned as the swing arm [Figs ! I(a)-(c)]. Also, for the kinematic chain shown in Fig. 10(b), three links can be assigned as the swing arm [Figs ! l(d)-(O]. For the kinematic chain shown in Fig. 10(c), two links can be assigned as the swing arm [Figs I I(g) and (h)]. For the kinematic chain shown in Fig. 10(d), two links can be assigned as the swing arm |Figs ! I(i) and (j)].

ACCEPTABLE SPECIALIZED KINEMATIC CHAINS

This step of the design methodology is to identify acceptable specialized kinematic chains subject to certain design constraints based on engineering reality and the designer's decisions. These constraints can be flexible and they are varied for different cases.

For our example, if there are no design constraints, the 10 specialized kinematic chains shown in Fig. I I are all acceptable. Here, we let the design constraint be that the swing arm must be adjacent to the fixed link. Then, only those six specialized kinematic chains shown in Figs I l(a), (b), (d), (f), (h) and (i) are acceptable.

(a)

(¢1

(b)

(d) (e)

Fig. 9. Specialized kinematic chain with fixed rink.

240 Ho~,-S~ Y~

(a)

{cl

(b)

Gr Ss~

(d)

Fi$. I0. Specialized kineamtic chains with fixed link and shock absorber.

(a) (b) (c)

(d) (f)

(z)

Gr S ~ s

(I)

(e) $s

Sw

(h)

{J) Fig. II. Atlas of specialized kinematic chains,

A ~ I o I ~ for a, mtive mmdmaimn ~ 241

A T L A S OF M E C H A N I S M S

The purpose of thil step is to IX~cularize each acceptable specialized Hnematic chain into its corresponding mechanism in a skeleton drawing. This is the reverse process of generalization and is done by applying the generalizing rules backward.

For those six specialized kinematic chains shown in Figs I l(a), (b), (d), (f), (h) and (i), their corresponding mechanisms are shown in Figs 12(a)--(f), respectively.

NEW M E C H A N I S M S

The last step of the design methodology is to identify new mechanisms from the created atlas of mechanisms by removing the existing designs. Designers can apply for patents for these new mechanisms.

For the six mechanisms shown in Fig. 12, that in Fig. 12(b) is the Kawasaki KX250 Uni-trak suspension, that in Fig. 12(e) is the Honda CR250 Pro-link suspension and that in Fig. 12(t") is the Suzuki RM250 Full-floater suspension, i.e. the original mechanism. Ther~'ore, we have throe new types of six-bar rear wheel suspension for off-road motorcycles as shown in Figs 12(a), (c) and (d).

S U M M A R Y

A systematic design methodology has been presented for the creation of all possible design con- cepts of mechanisms with required topological structures subject to certain designer's requirements

Ca) Cb)

Cc) Cd)

Ce) Cf) Fig. 12. Atlas of m~Imnisms.

242 H o m ~ Y ~

and constraints. The i x -ba r type rear tmspamion o f off-road motorcycles is adopted as an example to illustrate this design methodology. For detailed algnrithms of each design step, readers should refer to the cited references. The result o f this work provides design engineers with a powerful tool for generating new types of mechanisms to avoid existing designs which have patent protection.

R E F E R E N C E S 1. J. J. Chen, M.S. thes~ Department of Mechanical ~ Natiomd Chenli Kun8 Uaivmtity, Taimm (1982). 2. H. S. Yah and J. J. Chen, Prec. 6tit Appi. MedJ. Conf., St Louis, MO (1983); Mech. Mac& Theory ~(6), 597-600 (1985). 3. H. S. Yam and C. H. Hsu, J. CAinex $ec. Mech. Enffrs 4(1), !1-23 (1983). 4. C. H. Hsu and H. S. Yah, Prec. 4¢h ram. Cmf. CA/mint &x-. MecK F, qrs, ltsinse, hu, Taiwaa, 775-784 (1987). 5. H. S. Yam and L. C. Htieh, Prec. 1989 Int. Conf. Eqnf Des., l-larropte, pp. 757-766 (1989). 6. Y. W. Hwang" Ph.D. D~i~,ation, Department of Mechankal Engineering, National Cheng Kun| University, Taimm

(1990). 7. H. S. Yah and C. 14. l-hu. Prec. tst Int. Syrup. Dea. S.mt&, Tokyo, pp. 11-13 (1984). 8. H. S. Yah and Y. W. Hwang, d. Chbtex $ec. MecA. Enfrs 9, 191-198 (1988). 9. F. Harary and H. S. Yah, ASME Tram. d. Mech. Des. 112, 79-83 (1990).

10. H. S. Yah and Y. W. Hwang, Mat&. Cempta. Modelinff 13(8), 29-42 (1990). II. H. S. Yah and Y.W. Hwang, Prec. 1989 ASME Int. Cemput. E a ~ f Conf., Anaheim, CA, pp. 245-2.~ (1989). 12. H. S. Yah and Y. W. Hwang" Mech. Mech. Theory 26(6), 541-555.

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