Singularities of Robot Mechanisms: Numerical Computation and Avoidance Path Planning

Preface.- Notation.- List of Figures.- 1 Introduction.- 1.1 Historical Context.- 1.2 Assumptions and Scope.- 1.3 Reader's Guide.- 2 Singularity Types.- 2.1 Forward and Inverse Singularities.- 2.2 A Geometric Interpretation of Singularities.- 2.3 Lower-level Singularity Types.- 2.4 A Simple Mechanism with All Singularities.- 3 Numerical Computation of Singularity Sets.- 3.1 A Suitable Approach.- 3.2 Formulating the Equations of the Singularity Set.- 3.3 Isolating the Singularity Set.- 3.4 Visualising the Singularity Sets.- 3.5 Case Studies.- 4 Workspace Determination.- 4.1 The Need of a General Method.- 4.2 The Workspace and its Boundaries.- 4.3 Issues of Continuation Methods.- 4.4 Exploiting the Branch-and-Prune Machinery.- 4.5 Case Studies.- 5 Singularity-free Path Planning.- 5.1 Related Work.- 5.2 Formulating the Singularity-free C-space.- 5.3 Exploring the Singularity-free C-space.- 5.4 Case Studies.- 6 Planning with Further Constraints.- 6.1 Wrench-Feasibility Constraints.- 6.2 The Planning Problem.- 6.3 Proofs of the Properties.- 6.4 Case Studies.- 6.5 Details about the Wrench Ellipsoid.- 6.6 Extensions.- 7 Conclusions.- 7.1 Summary of Results.- 7.2 Future Research Directions.- References.- Index.- Author Index.