This research establishes the equation of a robot motion with parallel mechanisms based on the Lagrange multiplier method using residual generalized coordinates. Accordingly, the robot's equation of movement is a system of differential–algebraic equations (DAEs) consisting of joint coordinates and manipulator coordinates. This system of equations is transformed into a system of ordinary differential equations, with the variables being the coordinates of the manipulation stage. Proportional-Derivative (PD) control law in the Cartesian space is established to control the robot's motion, tracking a desired trajectory. A numerical simulation of Delta parallel robot tracking control was conducted with a specific data set to illustrate the established control method.