Abstract
This paper deals with the problem of synthesizing planar rational motions under the kinematic constraints of planar 6R closed chain. It follows our previous work on the synthesis of rational motions under the kinematic constraints of planar open chains. Planar quaternions are used to represent planar displacements. In this way, the problem of rational motion interpolation is transformed into that of rational curve interpolation, and the kinematic constraints of a planar 6R closed chain are transformed into geometric constraints for the rational interpolation. An algorithm for the constrained motion interpolation is developed that detects an extreme position on the rational motion that violates the kinematic constraints. This position is then modified so that it is in compliance with the kinematic constraints and is added to the list of positions to be interpolated. By restricting the kinematic constraints to 5R and 4R closed chains, the algorithm is also applicable to the problem of synthesizing planar rational motions for 5R and 4R closed chains.
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