Non overconstrained T3-type TPMs with uncoupled motions

Equation (1.15) indicates that non overconstrained solutions of T3-type TPMs with uncoupled motions and q independent loops meet the condition $\sum\nolimits_1^p {f_i } \, = \,3\, + \,6q\,$ along with S _F = 3, (R _F ) = (v ₁ ,v ₂ ,v ₃ ) and N _F = 0. They could have identical limbs or limbs with different structures and could be actuated by linear or rotating motors. Each operational velocity given by Eq. (1.19) depends on just one actuated joint velocity: v _i = v _i (q _i ), i = 1,2,3. The Jacobian matrix in Eq. (1.19) is a diagonal matrix.

They can be actuated by linear or rotating actuators which can be mounted on the fixed base or on a moving link. In the solutions presented in this section, the actuators are associated with a revolute joint mounted on the fixed base.