In this paper, a straightforward approach is developed to solve the nonlinear position equations for a linkage when a closed-form solution to some of the equations can be obtained. This is done with the aid of dependency checking concepts that organizes a system 2n equations and 2n unknowns (variables) into smaller sets of equations. When a set of two equations and two unknowns is obtained, the variables are analyzed using a closed-form (non-iterative) solution approach. Otherwise, an iterative approach such as the Newton-Raphson method is used for the analysis.

Issue Section:
Research Papers
Topics:
Linkages, Newton's method
1.
Brent
R. P.
,
1973
, “
Some Efficient Algorithms for Solving Systems of Nonlinear Equations
,”
SIAM Journal of Numerical Analysis
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327
–
344
.
2.
Brown
K. M.
,
1969
, “
A Quadratically Convergent Newton-Like Method Based Upon Gaussian Elimination
,”
SIAM Journal of Numerical Analysis
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4
, pp.
560
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569
.
3.
Broyden, C. G., 1970, “Recent Developments in Solving Nonlinear Algebraic Systems,” Numerical Methods for Nonlinear Algebraic Equations, P. Rabinowitz, ed., Gordon and Breach Science Publishers, New York.
4.
Chase
M. A.
,
1963
, “
Vector Analysis of Linkages
,”
ASME Journal of Engineering for Industry
, Ser. B, Vol.
55
, No.
3
, pp.
289
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297
.
5.
Eckhardt, H. D., 1984, “The Use of a Closed Form Algorithm in Planar Multi-Loop Linkage Analysis,” ASME paper 84-DET-136.
6.
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7.
Funabashi
H.
,
Ogawa
K.
, and
Hara
T.
,
1979
, “
Systematic Analyses of Velocity. Acceleration and Force of Planar Multilink Mechanisms
,”
Bulletin of the JSME
, Vol.
22
, No.
163
, pp.
86
–
92
.
8.
Galletti
C. U.
,
1986
, “
A Note on Modular Approaches to Planar Linkage Kinematic Analysis
,”
Mechanism and Machine Theory
, Vol.
21
, No.
5
, pp.
385
–
391
.
9.
Kinzel, G. L., and Chang, C-H., 1984, “The Analysis of Planar Linkages Using a Modular Approach,” Mechanism and Machine Theory, pp. 165–172.
10.
Lauw, B. T., 1988, “Computer Aided Design of Planar Mechanisms for Quasi-Static Forces,” M.S. Thesis, The Ohio State University.
11.
Lauw, B. T., et al., 1987, “Automatic Component Selection Algorithm For Kinematics Analyses,” Proceeding of the 1987 Applied Mechanism Conference, Vol. III, Session 9A, New Orleans, LA., December 6–9.
12.
Law, C. E., 1989, A Modular Approach to Computer-Aided Kinematic and Force Analysis of Planar Mechanisms with Lower Pair Joints,” M.S. Thesis, The Ohio State University.
13.
Nikravesh, P. E., 1988, Computer Aided Analysis of Mechanical Systems, Prentice Hall, Inc., New York.
14.
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15.
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16.
Prasad, A., and Kinzel, G. L., 1986, “A Case Selection Routine for Interactive Design Programs,” Proceedings of the 1986 International Computers in Engineering Conference, Vol. 2, pp. 95–100. Chicago, Ill., July 20–24.
17.
Retallack, L., and Kinzel, G. L., 1987, “A Study of Equation Order when Analyzing Planar Mechanism Using Vector-Loop Equations,” Proceedings of the 1987 Applied Mechanisms Conference, Vol. III, Session 9A, New Orleans, LA., December 6–9.
18.
Serrano, D., and Gossard, D. C., 1985, “Combining Mathematical Models with Geometric Models in CAE Systems,” Proceedings of the 1985 International Computers in Engineering Conference, Vol. I, pp. 277–284, Boston, Mass., August 4–8.
19.
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20.
Shigley, J. E., and Uicker, J. J., 1980, Theory of Machines and Mechanisms, McGraw-Hill Book Company, New York.
21.
Suh, C. H., and Radcliffe, C. W., 1978, Kinematics and Mechanism Design, Wiley, New York.
22.
Wilson, C. E., Saddler, J. P., and Michels, W. J., 1983, Kinematics and Dynamics of Machinery, Harper and Row Publishers, Inc., New York.
23.
Yakovlev, K. P., 1966, Handbook for Engineers, Vol II, Mechanics, Strength of Materials and the Theory of Mechanisms and Machines, Translated by J. J. Cornish, Pergamon Press, New York.
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