The Inverse Kinematic Problem Solution for the Slider-crank Mechanism-based Parallel Structure Manipulator with Three Degrees of Freedom

Abstract

The paper discusses a mechanism, which is a modification of the parallel kinematics mechanisms with three degrees of freedom (DOF) based on the slider-crank mechanism. The mechanism comprises a lower fixed and an upper movable platforms. The upper platform is connected to the lower one by six movable elements. Three of these elements are rods attached to the bases by means of spherical joints and three other ones have a slider-crank structure.An approach based on the mathematical modeling methods to solve an inverse kinematics is presented. The inverse kinematics problem was formulated as follows: to determine the value of crank angles, allowing us to achieve a specified position of the upper platform in space. To check the correctness of the solution was made an experimental unit. Also a set of required sensors and control boards were defined and an experiment design was provided. The paper presents comparison results of measurements with the calculated values of the generalized coordinates and draws appropriate conclusions. One of the distinctive features of the proposed approach is that the motor rotation angles are used as the generalized coordinates. So the paper formulates the possibilities to use the constructed model for the further development of control systems on its basis.

Keywords

• mathematical modeling
• parallel structure platform
• control systems