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.

Get full access to this article

View all access options for this article.

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.