Dynamic model of multi-DOF spherical mechanisms based on instantaneous pole axes

Spherical mechanisms have the peculiarity that a point (spherical motion center (SMC)) is at rest with respect to all the links. This feature makes the links perform only rotations around axes (instantaneous pole axes (IPAs)) passing through the SMC. IPAs’ locations fully describe their instantaneous kinematics and, in single-DOF mechanisms, uniquely depend on the mechanism configuration. In multi-DOF spherical mechanisms, IPAs’ locations are determinable by considering the single-DOF mechanisms generated from the multi-DOF ones by locking all the actuated joints but one. Exhaustive analytic/geometric techniques that determine all the IPAs’ locations of single-DOF spherical mechanisms by using only their configuration data are present in the literature. Here, a dynamic model of multi-DOF spherical mechanisms, which is general and strictly relates dynamic behavior and IPAs’ locations, is deduced by exploiting these results. This novel model can consider also possible frame motions. The proposed formulation lends itself better than others to satisfy dynamic requirements during mechanism design. Eventually, a relevant case study illustrates its effectiveness.