The dimensional synthesis of a spatial two revolute jointed dyad for path following tasks with applications to coupled serial chain mechanisms is presented. The precision point synthesis equations obtained using the rotation matrix approach form a rank-deficient linear system in the link-vector components. The nullspace of this rank-deficient linear system is derived analytically and interpreted geometrically. The nullspace vectors lead to the specification of additional constraints via the so-called auxiliary equations and to the solution of the linear system of equations. The geometry also allows the derivation of a closed form solution for the three design position problem. Finally, optimal path following by coupled R-R dyads is achieved by optimization over the free choice variables.

Issue Section:
Technical Papers
Keywords:
design engineering, kinematics, optimisation, Spatial Dyad, Coupled Serial Chain, Spatial Kinematic Synthesis, Optimization
Topics:
Chain, Design, Kinematics, Optimization, Rotation, Linear systems
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