Velocity, Acceleration, and Static-Force Analyses of Spatial Linkages

[+] Author and Article Information
J. Denavit

Northwestern University, Evanston, Ill.

R. S. Hartenberg

Northwestern University

R. Razi

Product Engineering Office, Ford Motor Company, Dearborn, Mich.

J. J. Uicker

Department of Mechanical Engineering and Astronautical Sciences, Northwestern University

J. Appl. Mech 32(4), 903-910 (Dec 01, 1965) (8 pages) doi:10.1115/1.3627334 History: Received October 26, 1964; Revised March 08, 1965; Online September 15, 2011


The algebraic method using 4 × 4 matrices is extended to the analysis of velocities, accelerations, and static forces in one-degree-of-freedom, single-loop, spatial linkages consisting of revolute and prismatic pairs, either singly or in combination. The methods are well suited for machine calculations and have been tested on a number of examples, one of which is presented. Velocities and accelerations are obtained by differentiation of the matrix-loop or position equation. Static forces are found by combining the method of virtual work with the matrix-loop equation to relate the virtual displacement of the load to given virtual deformations of the links.

Copyright © 1965 by ASME
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