Kinematic Modeling of a Two-link Robot with Flexible Arms

In this article, a complete kinematic modeling of a two -degree-of-freedom (DoF) mechanical manipulator with lateral vibrations is presented analytically. Kinematic design includes two sections of position and velocity in both forward and inverse approaches. The goal is to find the relation between the joint space and workspace of the manipulator which is a critical subject for dynamics and control analysis. It has been common to perform kinematic modeling of flexible link robots as a rigid structure; in this work, we consider flexibility of the arms in kinematic level. Links are considered as flexible beams with dependent boundary conditions on structure of the arms and motors; which vibrate in longitude, transverse and torsional directions. Here the transverse vibration is in the focus of the design as the most important source of the arm flexibilities. The motion has large and small deformations with low and high frequency, respectively. The small deformation of the system is effective on kinematic and workspace of the robot; hence, in this paper, with the aid of DenavitHartenberg (D-H) algorithm, Jacobian matrix and analytical solution of EulerBernoulli beam using discretization, a combination of two solutions for homogeneous transformation matrices are done which results in relations of forward and inverse kinematic of position and velocity of the arm. Simulations in MATLAB shows that flexible robots with enough small elastic modulus could result in considerable vibrations in kinematic; this could be very effective in dynamics and control followed by the generated model in this article