Hami Tourajizadeh - Assistant professor, Mechanical Enginnering Department, Faculty of Engineering, Kharazmi Universty, Tehran, Iran
Morteza Efafi - M. S. Student, Mechanical Enginnering Department, Faculty of Engineering, Kharazmi Universty, Tehran, Iran
Saeed RafeeNekoo - Independent Researcher, Tehran, Iran

In this article, a complete kinematic modeling of a two-degree-of-freedom (DoF) mechanical manipulator withlateral vibrations is presented analytically. Kinematic design includes two sections of position and velocity in bothforward and inverse approaches. The goal is to find the relation between the joint space and workspace of themanipulator which is a critical subject for dynamics and control analysis. It has been common to perform kinematicmodeling 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; whichvibrate in longitude, transverse and torsional directions. Here the transverse vibration is in the focus of the design as themost 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 thispaper, with the aid of Denavit-Hartenberg (D-H) algorithm, Jacobian matrix and analytical solution of Euler-Bernoullibeam using discretization, a combination of two solutions for homogeneous transformation matrices are done whichresults in relations of forward and inverse kinematic of position and velocity of the arm. Simulations in MATLAB showsthat flexible robots with enough small elastic modulus could result in considerable vibrations in kinematic; this could bevery effective in dynamics and control followed by the generated model in this article.

Flexible robotic manipulator, two-flexible-link, kinematic modeling, vibration