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1、The Inverse Kinematics Solutions of Industrial Robot Manipulators Serdar Kiiqiik Zafer Bingul Electronic and Computer Education Department of Mechatronics Engineering Kocaeli University, Kocaeli, Turkey e-mail :skucukkou.edu.tr Abstract The inverse kinematics problem of robot manipulators is desired
2、 to be solved analytically in order to have complete and simple solutions to the problem. This approach is also called as a closed form solution of robot inverse kinematics problem. In this paper, the inverse kinematics of sixteen industrial robot manipulators classified by Huang and Milenkovic I we
3、re solved in closed form. Each robot manipulator has an Euler wrist (Figure 1) whose three axes intersect at a common point. Basically, five trigonometric equations were used to solve the inverse kinematics problems. Robot manipulators can be mainly divided into four different group based on the joi
4、nt structure. In this work, the inverse kinematics solutions of SN (cylindrical robot with dome), CS (cylindrical robot), NR (articulated robot) and CC (selectively compliant assembly robot arm-SCARA, Type 2) robot manipulator belonging to each group mentioned above are given as an example. The numb
5、er of the inverse kinematics solutions for the other robot manipulator was also summarized in a table. 1. Introduction A robot manipulator is composed of a serial chain of rigid links connected to each other revolute or prismatic joints. A revolute joint rotates about a motion axis and a prismatic j
6、oint slide along a motion axis. Each robot joint location is usually defined relative to neighboring joint. The relation between successive joints is described by 4x4 homogeneous transformation matrices that have orientation and position data of robots. The number of those transformation matrices de
7、termines the degrees of fieedom of robots. The product of these transformation matrices produces final orientation and position data of a n degrees of fi-eedom robot manipulator. Given the sets of joint angles, calculate the position and orientation of the end-effector of the robot manipulator, is c
8、alled forward kinematics Z. Forward kinematics problem is straightforward and there is no complexity deriving the equations 5. Hence, there is always a forward kinematics solution of a robot manipulator. Tasks to be 0-7803-8599-3/04/$20.00 02004 IEEE 274 Kocaeli University Kocaeli, Turkey e-mail:zaf
9、erbkou.edu.tr performed by a robot manipulator are in the Cartesian space, whereas actuators work in joint space. Cartesian space includes orientation matrix and position vector. However, joint space is represented by joint angles. The conversion of the position and orientation of a robot manipulato
10、r end-effector from Cartesian space to joint space is called as inverse kinematics problem 3,4. This relationship between joint space and Cartesian space is illustrated in Figure 2. A Figure 1. The configuration of Euler wrist. The inverse kinematics problem of six joint robot manipulators has been
11、studied for decades. The reason of this study comes from widesprade use of six jointed robot manipulators in industry. The complexity of the inverse kinematics problem of industrial robot manipulators arises from their geometry and including nonlinear equations. Some other difficulties in inverse ki
12、nematics: kinematics equations are coupled and multiple solutions and singularities may exist. Matematical solutions for inverse kinematics problem may not always correspond to physical solutions and method of its solution depends on the robot configuration 6-81. There are three types of inverse kin
13、ematic solution: complete analytical solution (closed form solution), numerical solutions and semi-analitical solutions. In the first type, all of the joint variables are solved analytically according to given configuration data. Closed form solution is preferable because in many applications where
14、the manipulator supports or is to be supported by a sensory system, the results from kinematics computations Authorized licensed use limited to: TONGJI UNIVERSITY. Downloaded on July 06,2010 at 11:34:55 UTC from IEEE Xplore. Restrictions apply. need to be supplied rapidly in order to have control ac
15、tions. In the second type of solution, all of the joint variables are obtained iterative computational procedures. There are four disadvantages in these: a) incorrect initial estimations, b) before executing the inverse kinematics algorithms, convergence to the correct solution can not be guarantied
16、, c) multiple solutions are not known, d) there is no solution, if Jacobian matrix is singular 9. In the third type, some of the joint variables are determined analytically in terms of two or three joints variables and these joint variables computed numerically. Joint Figure 2. The schematic representation of forward and inverse kinematics. This paper is written following manner. In Section II, the pro
