An algebraic method for solving the closed-form direct kinematics of parallel mechanism based on ordered single-open-chain modeling

This paper presents an algebraic method for solving the direct kinematics of parallel mechanism based on ordered single-open-chain (SOC). Firstly, the mechanism is decomposed into a series of SOC units with different degrees of constraint based on the principle of mechanism composition. Then, the input-output position equations of the mechanism are established by the modeling principle based on ordered SOC. In addition, with the help of Mathematica, a nonlinear closed-form of direct kinematics is obtained. Finally, one example is given to verify this algebraic method.