Spatial Kinematic Chains [E-Book] : Analysis — Synthesis — Optimization / by Jorge Angeles.
Angeles, Jorge, (author)
Berlin, Heidelberg : Springer, 1982
XII, 370 p. online resource.
englisch
9783642488191
10.1007/978-3-642-48819-1
Full Text
Table of Contents:
  • 1 Mathematical Preliminaries
  • 1.0 Introduction
  • 1.1 Vector space, linear dependence and basis of a vector space
  • 1.2 Linear transformation and its matrix representation
  • 1.3 Range and null space of a linear transformation
  • 1.4 Eigenvalues and eigenvectors of a linear transformation
  • 1.5 Change of basis
  • 1.6 Diagonalization of matrices
  • 1.7 Bilinear forms and sign definition of matrices
  • 1.8 Norms, isometries, orthogonal and unitary matrices
  • 1.9 Properties of unitary and orthogonal matrices
  • 1.10 Stationary points of scalar functions of a vector argument
  • 1.11 Linear algebraic systems
  • 1.12 Numerical solution of linear algebraic systems
  • 1.13 Numerical solution of nonlinear algebraic systems
  • References
  • 2. Fundamentals of Rigid-Body Three-Dimensional Kinematics
  • 2.1 Introduction
  • 2.2 Motion of a rigid body
  • 2.3 The Theorem of Euler and the revolute matrix
  • 2.4 Groups of rotations
  • 2.5 Rodrigues’ formula and the Cartesian decomposition of the rotation matrix
  • 2.6 General motion of a rigid body and Chasles’ Theorem
  • 2.7 Velocity of a point of a rigid body rotating about a fixed point
  • 2.8 Velocity of a moving point referred to a moving observer
  • 2.9 General motion of a rigid body
  • 2.10 Theorems related to the velocity distribution in a moving rigid body
  • 2.11 Acceleration distribution in a rigid body moving about a fixed point
  • 2.12 Acceleration distribution in a rigid body under general motion
  • 2.13 Acceleration of a moving point referred to a moving observer
  • References
  • 3. Generalities on Lower-Pair Kinematic Chains
  • 3.1 Introduction
  • 3.2 Kinematic pairs
  • 3.3 Degree of freedom
  • 3.4 Classification of lower pairs
  • 3.5 Classification of kinematic chains
  • 3.6 Linkage problems in the Theory of Machines and Mechanisms
  • References
  • 4. Analysis of Motions of Kinematic Chains
  • 4.1 Introduction
  • 4.2 The method of Denavit and Hartenberg
  • 4.3 An alternate method of analysis
  • 4.4 Applications to open kinematic chains
  • References
  • 5. Synthesis of Linkages
  • 5.1 Introduction
  • 5.2 Synthesis for function generation
  • 5.3 Mechanism synthesis for rigid-body guidance
  • 5.4 A different approach to the synthesis problem for rigid-body guidance
  • 5.5 Linkage synthesis for path generation
  • 5.6 Epilogue
  • References
  • 6. An Introduction to the Optimal Synthesis of Linkages
  • 6.1 Introduction
  • 6.2 The optimisation problem
  • 6.3 Overdetermined problems of linkage synthesis
  • 6.4 Underdetermined problems of linkage synthesis subject to no inequality constraints
  • 6.5 Linkage optimisation subject to inequality constraints. Penalty function methods
  • 6.6 Linkage optimisation subject to inequality constraints. Direct methods
  • References
  • Appendix 1 Algebra of dyadics
  • Appendix 2 Derivative of a determinant with respect to a scalar argument
  • Appendix 4 Synthesis of plane linkages for rigid-body guidance.