In this work, we investigate the geometry and position kinematics of planar parallel manipulators composed of three GPR serial sub-chains, where G denotes a rolling contact, or geared joint, P denotes a prismatic joint, and R denotes a revolute joint. The rolling contact joints provide a passive one degree-of-freedom relative motion between the base and the prismatic links. It is shown, both theoretically and numerically, that when all the G-joints have equal circular contact profiles, there are at most 48 real forward kinematic solutions when the P joints are actuated. The solution procedure is general and can be used to predict and solve for the kinematics solutions of 3-GPR manipulators with any combination of rational contact ratios.
This paper deals with the sensitivity analysis of 3-RPR planar parallel manipulators (PPMs). First, the sensitivity coefficients of the pose of the manipulator moving platform to variations in the geometric parameters and in the actuated variables are expressed algebraically. Moreover, two aggregate sensitivity indices are determined, one related to the orientation of the manipulator moving platform and another one related to its position. Then, a methodology is proposed to compare 3-RPR PPMs with regard to their dexterity, workspace size and sensitivity. Finally, the sensitivity of a 3-RPR PPM is analyzed in detail and four 3-RPR PPMs are compared as illustrative examples.
SUMMARYThis paper is organized in two parts. In Part I, the wrench polytope concept is presented and wrench performance indices are introduced for planar parallel manipulators (PPMs). In Part II, the concept of wrench capabilities is extended to redundant manipulators and the wrench workspace of different PPMs is analyzed. The end-effector of a PPM is subject to the interaction of forces and moments. Wrench capabilities represent the maximum forces and moments that can be applied or sustained by the manipulator. The wrench capabilities of PPMs are determined by a linear mapping of the actuator output capabilities from the joint space to the task space. The analysis is based upon properly adjusting the actuator outputs to their extreme capabilities. The linear mapping results in a wrench polytope. It is shown that for non-redundant PPMs, one actuator output capability constrains the maximum wrench that can be applied (or sustained) with a plane in the wrench space yielding a facet of the polytope. Herein, the determination of wrench performance indices is presented without the expensive task of generating polytopes. Six study cases are presented and performance indices are derived for each study case.
Artificial Neural Network Based Forward Kinematics Solution for Planar Parallel Manipulators Passing through Singular Configuration
