The explicit formulation for the Jacobian matrix and its null space for an anthropomorphic manipulator arm with seven degrees of freedom are presented. The manipulability index of this redundant system, which is defined as the determinant of JJ/sup T/, is the Euclidian norm, of the generated null space vector.>

A discretized equation allows the acceleration terms to be changed to velocity terms in the definition of joint driving forces in robotic manipulators. An eleven degrees of freedom, three dimensional robotic manipulator is used in a numerical example to test the developed algorithm. Numerical and algorithmic stabilities are also discussed.

A simplified description of robotic manipulator is in terms of its zero reference position. It requires the specification of the joint axes directions and the coordinates of points locating the joint axes in the base coordinate system. Manipulator dynamics is developed in an extended zero reference position description. The recursive Newton-Euler formulations for the problems of inverse and direct dynamics are presented.

Numerical solution of the inverse kinematics of robots using modified Newton-Raphson (MNR) and modified predictor-corrector (MPC) algorithms is discussed. These modified algorithms are highly reliable and stable. Both algorithms always find a solution if a physically realizable robot configuration exists. They are also capable of approaching singular configurations of the robot as E = C εm, where E is the error between the theoretical and numerically computed singular joint values,\epsivis the convergence criteria, and C and m are appropriate constants. It is also shown that the modified predictor-corector (MPC) algorithm is 5-15 times faster than the modified Newton-Raphson (MNR) algorithm.