An algebraic method for the displacement analysis of linkages has been the subject of earlier publications [1, 2]. This method, based on the use of a symbolic notation, allows the application of matrix algebra to the study of displacements in linkages, and permits formulation of all the kinematic relations of a linkage in terms of matrix equations. Based on this earlier work, the present paper develops an iterative method for the solution of the matrix equations required in displacement analysis. A complete solution is given for simple-closed linkages consisting of revolute and prismatic pairs (and their combinations). A brief indication of how higher pairs and multiple-closed chains may be handled is also given. Particularly useful in spatial problems, since it does not depend on visualization, this approach is developed in a manner intended for digital-computer operation.
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June 1964
Research Papers
An Iterative Method for the Displacement Analysis of Spatial Mechanisms
J. J. Uicker, Jr.,
J. J. Uicker, Jr.
Department of Mechanical Engineering, Northwestern University, Evanston, Ill.
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J. Denavit,
J. Denavit
Northwestern University, Evanston, Ill.
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R. S. Hartenberg
R. S. Hartenberg
Northwestern University, Evanston, Ill.
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J. J. Uicker, Jr.
Department of Mechanical Engineering, Northwestern University, Evanston, Ill.
J. Denavit
Northwestern University, Evanston, Ill.
R. S. Hartenberg
Northwestern University, Evanston, Ill.
J. Appl. Mech. Jun 1964, 31(2): 309-314 (6 pages)
Published Online: June 1, 1964
Article history
Received:
March 14, 1963
Online:
September 15, 2011
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A commentary has been published:
Discussion: “An Iterative Method for the Displacement Analysis of Spatial Mechanisms” (Uicker, Jr., J. J., Denavit, J., and Hartenberg, R. S., 1964, ASME J. Appl. Mech., 31, pp. 309–314)
A commentary has been published:
Discussion: “An Iterative Method for the Displacement Analysis of Spatial Mechanisms” (Uicker, Jr., J. J., Denavit, J., and Hartenberg, R. S., 1964, ASME J. Appl. Mech., 31, pp. 309–314)
Citation
Uicker, J. J., Jr., Denavit, J., and Hartenberg, R. S. (June 1, 1964). "An Iterative Method for the Displacement Analysis of Spatial Mechanisms." ASME. J. Appl. Mech. June 1964; 31(2): 309–314. https://doi.org/10.1115/1.3629602
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