The analytical dynamic model of six-DOF industrial robotic manipulators of containing closed chain

A method for analytical dynamic modeling of six-DOF industrial robotic manipulators of containing closed chain is proposed. It is supposed that non-driving joints of the closed chain are disassembled of which motive relationships are substituted by constrained equations, then an equivalent system with additional constraints can be obtained. Based on Kane dynamic equations, the dynamic equations of the robotic manipulators in explicit form are derived. A part of variables (here independent and non-independent generalized coordinates) are treated as symbols, and then the numeric-symbolic expressions of the dynamic model matrices are obtained. At last, a numerical example is given to demonstrate this method.