Unification and simplification of velocity/acceleration of limited-dof parallel manipulators with linear active legs

A unified and simple approach is proposed for solving inverse/forward velocity and acceleration of the limited-dof PKMs (parallel kinematic machines) with linear active legs. First, a general PKM with n active legs is constructed and some formulae for solving inverse displacement are derived. Second, the poses of the constrained wrench are determined and the formulae for solving auxiliary Jacobian/Hessian matrices and statics are derived. Third, some formulae are derived for solving the general velocity/acceleration, the 6 × 6 Jacobian matrix and the 6 × 6 × 6 Hessian matrix. Finally, the solving procedure is illustrated by applying it to a 3-SPR, a 4SPS + SPR and a 3-UPU PKMs.