Synthesis of Spatial CC Dyads and 4C Mechanisms for Pick & Place Tasks with Guiding Locations

Abstract

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for spatial CC kinematic chains is presented. The methodology uses an analytic representation of the spatial CC dyad’s rigid body constraint equation in combination with an algebraic geometry formulation of the perpendicular screw bisector to yield designs that exactly reach the prescribed pick & place locations while approximating an arbitrary number of guiding locations. The result is a dimensional synthesis technique for mixed exact and approximate motion generation that utilizes only algebraic geometry and does not require the use of any iterative optimization algorithms or a metric on spatial displacements. An example that demonstrates the synthesis technique is included.