An Iterative Method for the Displacement Analysis of Spatial Mechanisms

[+] Author and Article Information
J. J. Uicker

Department of Mechanical Engineering, Northwestern University, Evanston, Ill.

J. Denavit, R. S. Hartenberg

Northwestern University, Evanston, Ill.

J. Appl. Mech 31(2), 309-314 (Jun 01, 1964) (6 pages) doi:10.1115/1.3629602 History: Received March 14, 1963; Online September 15, 2011


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.

Copyright © 1964 by ASME
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