Dynamic Analysis Of A 3-DOF Cartesian Parallel Manipulator

Parallel manipulators have been studied extensively for applications that require high speed, accuracy, and stiffness. However, most of manipulators have some disadvantages such as complex kinematics, small workspace and dynamics because of cross-coupling between links. To overcome these shortcomings, a manipulator with fewer than six degrees of freedom has received much attention due to their simple kinematics and uncoupled motions.In this paper, a 3-DOF translational parallel manipulator called 3-PRRR Cartesian parallel mechanism (CPM) is studied. The manipulator consists of a moving platform that is connected to a fixed base by three limbs. Each limb is made up of one cylindrical and two revolute joints and all joint axes are parallel to one another, and three limbs are orthogonal like a conventional X-Y-Z Cartesian mechanism.Based on screw theory, the degree of freedom of the manipulator is simply obtained. Then two actuation methods are discussed. For rotary actuation method, the forward kinematics leads to an eighth-degree polynomial and there are many singular points with the workspace. On the other hand, for the linear actuation method, there exists a one to one correspondence between the input and output displacements of the manipulator. In the other words, the kinematic Jacobian matrix is identity. So the linear actuation method is chosen for further analysis and prototype development. Moreover,a static force analysis is completed.An explicit form of the coupling forces among the limbs of the CPM has been calculated using the Newton-Euler method for each limb. With the coupling forces, the dynamic model of the Cartesian parallel mechanism is derived using the Lagrange-D'Alembert method for each direction. A visual prototype of the CPM is built in the software of SolidWorks and the kinematic and dynamic simulations are shown in the module of CosmosMotion. By comparison of the outcomes obtained in the dynamic equation, the accuracy and consistency of simulations and dynamic equation is verified. The mass, inertia tensor and velocity of limbs are the primary factors influencing dynamic performance.Finally, a prototype CPM driven by the servo motor and controlled by PC has been constructed using the above outcomes.