Dynamic modeling of SCARA robot based on Udwadia–Kalaba theory

With the aim of dynamic modeling of the SCARA robot subjected to space trajectory constraint to satisfy repetitive tasks with higher accuracy, a succinct and explicit equation of motion based on Udwadia–Kalaba theory is established. The trajectory constraint, which is regarded as the external constraints imposed on the system, is integrated into the dynamic modeling of the system dexterously. The explicit expression of constraint torques required to satisfy constraints and explicit dynamic equation of the system without Lagrange multiplier are obtained. However, constraint violation arises when the initial conditions are incompatible with the constraint equations. Baumgarte stabilization method is considered for constraint violation suppression. Simulations of the varying law of the generalized coordinate variables and the trajectories of the SCARA robot are performed to demonstrate the simplicity and accuracy of the method.