A homogeneous matrix approach to 3D kinematics and dynamics—II. Applications to chains of rigid bodies and serial manipulators

In this paper we present applications of the new approach to the kinematic and dynamic analysis of systems of rigid bodies presented in Part I. An extension of the method to the Lagrangian formulation of the dynamics of chains of rigid bodies is also presented. The kinematic and dynamic analysis is preformed for a generic serial manipulator either in open and closed loop. Two numerical examples concerning an open loop and a closed loop are presented too. Two software packages based on our approach are also briefly introduced.

[1]  T. S. Sankar,et al.  Development of efficient closed-form dynamic equations for robot manipulators using parallel and perpendicular concepts , 1993 .

[3]  Krzysztof Kozlowski,et al.  Computational requirements for a discrete Kalman filter in robot dynamics algorithms , 1993, Robotica.

[4]  D. Chevallier,et al.  Lie algebras, modules, dual quaternions and algebraic methods in kinematics , 1991 .

[5]  J. Casey,et al.  A tensor method for the kinematical analysis of systems of ridid bodies , 1986 .

[6]  M. Vukobratovic,et al.  Applied Dynamics of Manipulation Robots , 1989 .

[7]  Gr Geert Veldkamp On the use of dual numbers, vectors and matrices in instantaneous, spatial kinematics , 1976 .

[8]  K. H. Hunt,et al.  Spatial motion-I: Points of inflection and the differential geometry of screws , 1992 .

[9]  A Complete Notation for Dual Velocity , 1992 .

[10]  C. Spoor,et al.  Rigid body motion calculated from spatial co-ordinates of markers. , 1980, Journal of biomechanics.

[11]  K. H. Hunt,et al.  Spatial motion-II: Acceleration and the differential geometry of screws , 1992 .

[12]  R. Paul Robot manipulators : mathematics, programming, and control : the computer control of robot manipulators , 1981 .

[13]  Yueh-Jaw Lin,et al.  Simplification of manipulator dynamic formulations utilizing a dimensionless method , 1993, Robotica.

[14]  T. S. Sankar,et al.  Fast inverse dynamics computation in real-time robot control , 1992 .

[15]  Hendrik Van Brussel,et al.  Software for solving the inverse kinematic problem for robot manipulators in real time , 1983 .

[16]  Barry I. Soroka Advanced software in robotics , 1987, IEEE J. Robotics Autom..

[17]  Kenneth H. Hunt Special configurations of robot-arms via screw theory , 1986, Robotica.

[18]  Sunil K. Agrawal Multibody Dynamics: A Formulation Using Kane’s Method and Dual Vectors , 1993 .