A few words about the series "Scientific Fundamentals of Robotics" should be said on the occasion of publication of the present monograph. This six-volume series has been conceived so as to allow the readers to master a contemporary approach to the construction and synthesis of con­ trol for manipulation ~obots. The authors' idea was to show how to use correct mathematical models of the dynamics of active spatial mecha­ nisms for dynamic analysis of robotic systems, optimal design of their mechanical parts based on the accepted criteria and imposed constraints, optimal choice of actuators, synthesis of dynamic control algorithms and their microcomputer implementation. In authors' oppinion this idea has been relatively successfully realized within the six-volume mono­ graphic series. Let us remind the readers of the books of this series. Volumes 1 and 2 are devoted to the dynamics and control algorithms of manipulation ro­ bots, respectively. They form the first part of the series which has a certain topic-related autonomy in the domain of the construction and application of the mathematical models of robotic mechanisms' dynamics.

Inhalt

1 Kinematic Equations.- 1.1. Introduction.- 1.2. Definitions.- 1.3. Manipulator hand position.- 1.3.1. Rodrigues formula approach.- 1.3.2. Homogeneous transformations.- 1.3.3. Spherical coordinates.- 1.3.4. Cylindrical coordinates.- 1.4. Manipulator hand orientation.- 1.4.1. Euler angles.- 1.4.2. Euler parameters.- 1.5. Manipulator hand velocities.- 1.5.1. Recursive and nonrecursive relations for linear and angular velocities.- 1.5.2. The Jacobian matrices.- 1.6. Summary.- 2 Computer-aided Generation of Kinematic Equations in Symbolic Form.- 2.1. Introduction.- 2.2. Symbolic kinematic equations.- 2.2.1. Backward and forward recursive relations.- 2.2.2. Kinematic equations for the UMS-3B manipulator.- 2.2.3. Backward recursive symbolic relations.- 2.2.4. Forward recursive symbolic relations.- 2.2.5. Treatment of revolute joints with parallel joints axes.- 2.3. The Jacobian matrix with respect to the hand coordinate frame.- 2.3.1. The Jacobian for the UMS-3B manipulator.- 2.3.2. Recursive symbolic relations for the Jacobian with respect to the hand coordinate frame.- 2.3.3. The Jacobian columns corresponding to parallel joints.- 2.4. The Jacobian matrix with respect to the base coordinate frame.- 2.4.1. The Jacobian for the UMS-3B manipulator.- 2.4.2. Recursive symbolic relations for the Jacobian with respect to the base coordinate frame.- 2.4.3. The Jacobian columns corresponding to parallel joints.- 2.5. Program implementation, numerical aspects and examples.- 2.5.1. Block-diagram of the program for the symbolic model generation.- 2.5.2. Examples.- 2.5.3. Numerical aspects.- 2.6. Summary.- Appendix I Direct Kinematic Problem for the Arthropoid Manipulator.- Appendix II The Jacobian with Respect to the Hand Coordinate Frame for the Arthropoid Manipulator.- Appendix III The Jacobion with Respect to the Base Coordinate Frame for the Arthropoid Manipulator.- 3 Inverse Kinematic Problem.- 3.1. Introduction.- 3.2. Analytical solutions.- 3.3. Numerical solutions.- 3.4. Summary.- 4 Kinematic Approach to Motion Generation.- 4.1. Introduction.- 4.2. Manipulation task.- 4.3. Trajectory planning.- 4.4. Motion between positions.- 4.4.1. Joint-interpolated motion.- 4.4.2. External coordinates motion.- 4.5. Procedurally defined motion.- 4.6. Summary.- 5 Dynamic Approach to Motion Generation.- 5.1. Introduction.- 5.2. Manipulation system dynamic model.- 5.3. An overview of methods for dynamic motion synthesis.- 5.4. Determination of the energy optimal velocity distribution using dynamic programming.- 5.5. Quasioptimal nominal trajectory synthesis using decentralized system model.- 5.6. Summary.- 6 Motion Generation for Redundant Manipulators.- 6.1. Introduction.- 6.2. Kinematic methods for redundant manipulator motion generation.- 6.3. Energy optimal motion synthesis.- 6.4. Obstacle avoidance using redundant manipulators.- 6.5. An algorithm for redundant manipulator motion synthesis in the presence of obstacles.- 6.6. Summary.- References.