This paper presents a generalized approach to the singularity analysis of mechanisms with arbitrary kinematic chains and an equal number of inputs and outputs. The instantaneous kinematics of a mechanism is described by means of a velocity equation, explicitly including not only the input and output velocities but also the passive-joint velocities. A precise definition of singularity of a general mechanism is provided. On the basis of the six types of singular configurations and the motion space interpretation of kinematic singularity introduced in the paper, a comprehensive singularity classification is proposed.
A Unifying Framework for Classification and Interpretation of Mechanism Singularities
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Zlatanov, D., Fenton, R. G., and Benhabib, B. (December 1, 1995). "A Unifying Framework for Classification and Interpretation of Mechanism Singularities." ASME. J. Mech. Des. December 1995; 117(4): 566–572. https://doi.org/10.1115/1.2826720
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