Spatial PMs with coupled planar motion of the moving platform

Abstract

The solutions of spatial parallel mechanism with planar motion of the moving platform have in their structure at least one spatial limb. In the general case, in a spatial parallel robotic manipulator (SPM) with coupled planar motions of the moving platform each operational velocity depends in the general case on three actuated joint velocities. In this section we focus on the solutions with decoupled rotation of the moving platform with ${\it v}_{\it 1}={\it v}_{\it 1}({\it\dot{q}_{\it1}},{\it\dot{q}_{\it 2}}), {\it v}_{\it 2}={\it v}_{\it2}({\it\dot{q}_{\it 1}},{\it\dot{q}_{\it 2}})$and$\omega_\delta=\omega_\delta({\it\dot{q}}_{\it 3})$In these solutions, the Jacobian matrix in Eq. (6.1) is not triangular and the parallel robot is considered withcoupled motions. They have just a few partially decoupled motions.