Kinematic analysis of platform-type robotic manipulators.

摘要

New methods are developed for the kinematic analysis of serial and platform-type parallel robotic manipulators, including forward and inverse kinematic solutions, singularity identifications and workspace evaluation. Differences between serial and platform-type parallel manipulators, which can provide substantially improved end-point rigidity compared with the conventional serial robotic arms, are addressed.; The problem of determining the screw parameters of rigid body motion from initial and final position data is discussed, as a basis to search for a general and efficient procedure to solve the complex forward kinematics problem of platform-type manipulators.; Several Screw-Theory based approaches for solving the inverse instantaneous problem of 6 DOF serial manipulators are studied and compared in terms of their computational efficiency, accuracy, sensitivity to data error and capability of dealing with singularities. A modified Vector Decomposition method is then proposed for solving the IIK problem and for singularity analysis of serial kinematic chains, the method is especially effective when applied to the wrist partitioned serial manipulators, which are essential components to any platform-type parallel manipulators.; By using the data of three point positions, velocities, and accelerations of the end effector a general method is developed for solving the forward kinematics problem, including position, velocity and acceleration kinematics, of platform-type manipulators. The solution procedure can be applied to a wide variety of platform-type manipulators such as the 6 DOF Steward Platform manipulator and other models. It is found that while the solution for the forward position kinematics of a platform-type manipulator can be obtained by solving a non-linear system of equations, the closed-form solutions for forward rate and acceleration kinematics can be found by solving a system of linear equations.; Based on the proposed kinematic formulations, an algorithm for detecting the boundaries of reachable workspace of platform-type manipulators is introduced, using a new concept of the Geometric Envelope. As the algorithm is based on the relatively simple inverse kinematic solution of platform-type manipulators, it is, in general, more efficient and easier to implement than any other existing methods for this purpose.; Singular configurations of platform-type manipulators are discussed and a general analytical condition for configuration singularity is derived, based on the forward rate kinematics of platform-type manipulators. It is believed that this is one of the most general analytical expressions so far for singular configurations of a platform-type parallel manipulator.