First- and second-order kinematics-based constraint system analysis and reconfiguration identification for the queer-square mechanism

Reconfiguration identification of a mechanism is essential in design and analysis of reconfigurable mechanisms. However, reconfiguration identification of a multiloop reconfigurable mechanism is still a challenge. This paper establishes the first- and second-order kinematic model in the queer-square mechanism to obtain the constraint system by using the sequential operation of the Lie bracket in a bilinear form. Introducing a bilinear form to reduce the complexity of first- and second-order constraints, the constraint system with first- and second-order kinematics of the queer-square mechanism is attained in a simplified form. By obtaining the solutions of the constraint system, six motion branches of the queer-square mechanism are identified and their corresponding geometric conditions are presented. Moreover, the initial configuration space of the mechanism is obtained.