Singularities in Motion and Displacement Functions for the RCRCR Linkage

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Abstract
The previously proposed approach (Litvin et al, 1986b) is applied for determination of singularities in motion and displacement functions for the RCRCR linkage. Singularities in motion occur at positions where an overconstrained group of links becomes movable at least locally while the driving link is fixed. The determination of displacement functions is based on modeling of the linkage by two open kinematic chains formed by: (a) links of an overconstrained group of links and (b) the driving link and the frame. Conditions of “assembly” of the open chains provide invariants—scalar products—that yield the appropriate equations that relate the parameters in motion of the driving link and the overconstrained group of links. The number of linkage configurations is proposed to determine through the number of singularity positions that are simulated with a certain combination of the linkage design parameters.

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