Synthesis of 7-R Spatial Motion Generators with Prescribed Crank Rotations and Elimination of Branching

Abstract

The paper presents conditions for avoidance of branching in the synthesis of 7-R spatial mechanisms. These conditions are based on the theory of linearly dependent screws by Hunt (1978) and on the theory about the existence of tangent loci in the so-called stationary configuration of the mechanisms (Sandor and Zhuang 1984a and b). First, the conditions for stationary configuration are obtained on the basis of the above-mentioned theories. Then, since the related branches are at both sides of the special canfiguration, corresponding conditions for avoidance of branching are obtained. Finally, we present a numerical example of the synthesis of a 7-R spatial motion generator with prescribed finitely separated positions, prescribed crank rotations, and with application of branching defect avoidance.

References

Filemon, E. 1971 (Sept. 13-20, Kupari, Yugoslavia). In addition to the branching theory Proc. 3rd World Congress for the Theory of Machines and Mechanics, Vol. D: 63-78.

Filemon, E. 1972. Useful ranges of centerpoint curves of design of crank and rocker linkages Mechanism and Machine Theory 7:47- 53.

Gupta, K.C. 1980. Synthesis of position, path and function generating four-bar mechanisms with completely rotatable driving links Mechanism and Machine Theory 15:93-101.

Gupta, K.C. 1984 (July 11-13, Tokyo, Japan). Applications of inequality manipulation in defect-free mechanism synthesis. Proc. Int. Symp Design and Synthesis: 649-656.

Gupta, K.C. , and Tinubu, S. 1983

(Dec.). Synthesis of bimodal function generating mechanisms without branch defect

Trans. ASME, J. Mechanisms, Transmissions and Automation in Design 105(4):641-648.

Hooke, R. , and Jeeves, T.A. 1961. "Direct search" solution of numerical and statistical problems J. Assn. for Computing Machinery 8:212-229.

Hunt, K.H. 1978. Kinematic geometry of mechanisms London: Oxford University Press.

Sandor, G.N. , and Erdman, A.G. 1984. Advanced mechanism design: analysis and synthesis , Vol. 2. Englewood Cliffs, N.J. : Prentice-Hall.

Sandor, G.N. , and Zhuang, X. 1984a (Sept.). On the elimination of the branching problem in the synthesis of spatial motion generators with spheric joints, part I: theory Trans. ASME, J. Mechanisms, Transmissions and Automation in Design 106(3):312-318.

10.

Sandor, G.N. , and Zhuang, X. 1984b (Sept.). On the elimination of the branching problem in the synthesis of spatial motion generators with spheric joints, part II: application Trans. ASME, J. Mechanisms, Transmissions and A utomation in Design 106(3):319-326.

11.

Tinubu, S.O. , and Gupta, K.C. 1984

(Sept.). Optimal synthesis of function generators without the branch defect

Trans. ASME, J. Mechanisms, Transmissions and Automation in Design 106(3):348-354.

12.

Waldron, K.J. 1974a. Range of joint rotation in planar four-bar synthesis for finitely separated positions, part 1: the multiple branch problems ASME Paper, 74-DET-108.

13.

Waldron, K.J. 1974b. Range of joint rotation in planar four-bar synthesis for finitely separated positions, part 2: elimination of unwanted Grashof configuration ASME Paper, 74-DET-109.

14.

Waldron, K.J. 1975

(Nov., Chicago). Graphical Burmester design of four-bar linkage for a specified position order and with all positions reachable without disconnection

Proc. 4th OSU Applied Mechanisms Conf , pp. 8-1-8-13.

15.

Waldron, K.J. 1976

(Feb.). Elimination of the branch problem in graphical Burmester mechanism synthesis for four finitely separated positions

Trans. ASME, J. Engineering for Industry, Series B, 98(l):176 - 182.

16.

Waldron, K.J. 1977. Graphical solution of the branch and order problem of linkage synthesis for multiply separated positions Trans. ASME, J. Engineering for Industry, Series B, 99:591-597.

17.

Waldron, K.J. , and Strong, R.T. , 1978a. Improved solutions of the branch and order problems of Burmester linkage synthesis Mechanism and Machine Theory 13(2):199-207.

18.

Waldron, K.J. , and Strong, R.T. 1978b (Oct.) Improved precision position mechanism synthesis . NSF Final Report, No. TR-12, University of Houston.

19.

Waldron, K.J. , and Stevensen, E.N. Jr. 1980. Elimination of branch, Grashof, and order defects in path-angle generation and function generation synthesis J. Mechanism and Machine Theory 15:93-101.