This paper presents the application of dual-number matrices to the formulation of displacement equations of robot manipulators with completely general geometry. Dual-number matrices make possible a concise representation of link proportions and joint parameters; together with the orthogonality properties of the matrices we are able to derive, in a systematic manner, closed-form solutions for the joint displacements of robot manipulators with special geometry as illustrated by three examples. It is hoped that the method presented here will provide a meaningful alternative to existing methods for formulating the inverse kinematics problem of robot manipulators.
Application of Dual-Number Matrices to the Inverse Kinematics Problem of Robot Manipulators
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Pennock, G. R., and Yang, A. T. (June 1, 1985). "Application of Dual-Number Matrices to the Inverse Kinematics Problem of Robot Manipulators." ASME. J. Mech., Trans., and Automation. June 1985; 107(2): 201–208. https://doi.org/10.1115/1.3258709
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