Abstract
Parallel Kinematic Machines (PKMs) are being widely used for precise applications to achieve complex motions and variable poses for the end effector tool. PKMs are found in medical, assembly and manufacturing industries where accuracy is necessary. It is often desired to have a compact and simple architecture for the robotic mechanism. In this paper, the kinematic and dynamic analysis of a novel 3-PRUS (P: prismatic joint, R: revolute joint, U: universal joint, S: spherical joint) parallel manipulator with a mobile platform having 6 Degree of Freedom (DoF) is explained. The kinematic equations for the proposed spatial parallel mechanism are formulated using the Modified Denavit-Hartenberg (DH) technique considering both active and passive joints. The kinematic equations are used to derive the Jacobian matrix of the mechanism to identify the singular points within the workspace. A Jacobian based stiffness analysis is done to understand the variations in stiffness for different poses of the mobile platform and further, it is used to decide trajectories for the end effector within the singularity free region. The analytical model of the robot dynamics is presented using the Euler-Lagrangian approach with Lagrangian multipliers to include the system constraints. The gravity and inertial forces of all links are considered in the mathematical model. The analytical results of the dynamic model are compared with ADAMS simulation results for a pre-defined trajectory of the end effector.
Highlights
Robot manipulators can be broadly classified into open or closed depending upon the connections between each link and the end effector
A Parallel Manipulator (PM) has the end effector connected by several independent kinematic chains that enable superior rigidity and precision over serial manipulators [1, 2]
Even though the computation involved with the DH model is slightly higher, the singularity analysis performed with the DH model will be more effective than that obtained from the Screw theory model. This is because the analysis considers the singularity induced due to both active and passive joints
Summary
Robot manipulators can be broadly classified into open or closed depending upon the connections between each link and the end effector. Screw Theory [14, 16, 26] is another well-established methodology which is found in many literatures to obtain the kinematic model for parallel mechanisms According to this method, it has only two coordinate frames of which one is located at the base and the other is at the end-effector. The pose of the end effector tip is determined separately from the global frame {O2} by assuming each leg to be individual serial chains. (4), (5) and (6) can be equated to the desired pose matrix to couple the three legs and obtain the closed-form inverse kinematic solution for the 3-PRUS manipulator. The average time taken to solve a set of equations by the LMA algorithm is 42 s using an Intel Core i7 processor
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