Minimum inertial parameters of robots with parallelogram closed-loops

A symbolic method of determining the minimum set of inertial parameters of robots containing parallelogram closed loops is presented. The solution is obtained by determining the minimum inertial parameters of an equivalent tree structure robot and then taking into account the constraint equations of the closed loops to get the global minimum inertial parameters. Direct general relations that do not require the calculation of the dynamic model of the system are obtained for the two steps. The method is general whatever the values of the geometric parameters