High efficient inverse dynamic calculation approach for a haptic device with pantograph parallel platform

This article presents a novel inverse dynamic calculation approach for a haptic device with pantograph parallel platform. This approach uses vector differential equations in kinematics analysis, hence deriving the explicit expressions of all links' linear velocities, linear accelerations, angular velocities, and angular accelerations. In contrast to the regular influence coefficient method, the kinematics expressions presented herein avoid the large calculation load of matrix inverse operation, which is crucial to real-time computation. Kane's equation is employed to establish the inverse dynamic calculation expression for the special architecture of hybrid series-parallel branch. The elements of velocity wrench of the top plate are chosen as the generalized velocities. After deriving the matrixes of partial linear velocity and partial angular velocity, the inverse dynamic equation in explicit form is obtained. Compared with the results calculated by ADAMS, the precision of this calculation approach is validated. Given that it is highly efficient and accurate, this approach is more suitable for real-time compute-torque control, especially for mechanisms with hybrid series-parallel branches.