Typical industrial robots have six or fewer DOF. With six DOF, the robot can, within its work reach arbitrary positions and orientations. At the edge of the work envelope, a six-DOF robot can att one orientation. To increase the geometric dexterity of the manipulator, it is useful to consider rob more than six DOF, i.e., redundant robots. These robots are highly dexterous and can use the extra DOF in many ways: avoidance obstacle, joint torque minimization, kinematic singularity(points where the manipulator cannot move in certain directions) avoidance, bracing strategies where part of the arm is braced against a structure,which raises the lowest structural resonant frequency of the arm, etc. while the redundant manip- ulator configuration has many desirable properties, the geometric complexity has limited their application in industry. For any of the six standard robot configurations, the orientation capability of the major linkages is severel limited. Thus, it is critical to provide additional joints, known as the minor linkages, to provide the capability of varied orientations for a given position. Most robots include a three-DOF revolute joint wrist that is connected to the last link of the major linkages. The three revolute axes will be orthogonal and will usually intersect in common point, known as the wrist center point. Then, the kinematic equations of the manipulator can be partitioned into locating the Cartesian position of the wrist center point and then determining the orientation of a Cartesian frame fixed to the wrist axes Conclusions Each of the six standard configurations has specific advantages and disadvantages. When choosing a manipulator for a task, the properties of the manipulator geometry are one of the most important considerations. If the manipulator will be used for a wide variety of tasks, one may need to trade off performance for any given task for the flexibility that will allow the manipulator to work for the various tasks. In such a case, a more flexible geometry should be considered. The future of robotics will be interesting. With the steady increase in compu tional capabilities, the more complex geometries, including redundant and multiple robots, are beginning to see increased applications in industry. Defining Terms Degrees of freedom: The number of degrees of freedom(DOF)of a manipulator is the number of independent position variables that must be specified in order to locate all parts of the bulator. For a typical industrial manipulator, the number of joints equals the number of doF. Kinematics: The kinematics of the manipulator refers to the geometric properties of the manipulator. Forward kinematics is the computation of the Cartesian position and orientation of the robot end-effector given coordinates. Inverse kinematics is the comp Cartesian position and orientation of the end-effector. The inverse kinematic computation may not be possible in closed form, may have no solution, or may have multiple solutions. Redundant manipulator: A redundant manipulator contains more than six DOF. Singularity: A singularity is a location in the workspace of the manipulator at which the robot loses one or more DOF in Cartesian space, 1. e, there is some direction(or directions) in Cartesian space along which it is impossible to move the robot end-effector no matter which robot joints are moved. Related Topic 101.2 Dynamics and Control References R.G. Bonitz and T.C. Hsia,"Internal force-based impedance control for cooperating manipulators, " IEEE Transactions on robotics and Automation, Feb. 1996 J.J. Craig, Introduction to Robotics: Mechanics and Control, Reading, Mass. Addison-Wesley, 1986 A J. Critchlow, Introduction to robotics, New York: Macmillan, 1985 c 2000 by CRC Press LLC© 2000 by CRC Press LLC Typical industrial robots have six or fewer DOF. With six DOF, the robot can, within its work envelope, reach arbitrary positions and orientations. At the edge of the work envelope, a six-DOF robot can attain only one orientation. To increase the geometric dexterity of the manipulator, it is useful to consider robots with more than six DOF, i.e., redundant robots. These robots are highly dexterous and can use the extra DOF in many ways: avoidance obstacle, joint torque minimization, kinematic singularity (points where the manipulator cannot move in certain directions) avoidance, bracing strategies where part of the arm is braced against a structure, which raises the lowest structural resonant frequency of the arm, etc. While the redundant manip￾ulator configuration has many desirable properties, the geometric complexity has limited their application in industry. For any of the six standard robot configurations, the orientation capability of the major linkages is severely limited. Thus, it is critical to provide additional joints, known as the minor linkages, to provide the capability of varied orientations for a given position.Most robots include a three-DOF revolute joint wrist that is connected to the last link of the major linkages. The three revolute axes will be orthogonal and will usually intersect in a common point, known as the wrist center point. Then, the kinematic equations of the manipulator can be partitioned into locating the Cartesian position of the wrist center point and then determining the orientation of a Cartesian frame fixed to the wrist axes. Conclusions Each of the six standard configurations has specific advantages and disadvantages.When choosing a manipulator for a task, the properties of the manipulator geometry are one of the most important considerations. If the manipulator will be used for a wide variety of tasks, one may need to trade off performance for any given task for the flexibility that will allow the manipulator to work for the various tasks. In such a case, a more flexible geometry should be considered. The future of robotics will be interesting. With the steady increase in compu￾tational capabilities, the more complex geometries, including redundant and multiple robots, are beginning to see increased applications in industry. Defining Terms Degrees of freedom: The number of degrees of freedom (DOF) of a manipulator is the number of independent position variables that must be specified in order to locate all parts of the manipulator. For a typical industrial manipulator, the number of joints equals the number of DOF. Kinematics: The kinematics of the manipulator refers to the geometric properties of the manipulator. Forward kinematics is the computation of the Cartesian position and orientation of the robot end-effector given the set of joint coordinates. Inverse kinematics is the computation of the joint coordinates given the Cartesian position and orientation of the end-effector. The inverse kinematic computation may not be possible in closed form, may have no solution, or may have multiple solutions. Redundant manipulator: A redundant manipulator contains more than six DOF. Singularity: A singularity is a location in the workspace of the manipulator at which the robot loses one or more DOF in Cartesian space, i.e., there is some direction (or directions) in Cartesian space along which it is impossible to move the robot end-effector no matter which robot joints are moved. Related Topic 101.2 Dynamics and Control References R.G. Bonitz and T.C. Hsia, “Internal force-based impedance control for cooperating manipulators,” IEEE Transactions on Robotics and Automation, Feb. 1996. J.J. Craig, Introduction to Robotics: Mechanics and Control, Reading, Mass.: Addison-Wesley, 1986. A. J. Critchlow, Introduction to Robotics, New York: Macmillan, 1985