the manipulator becomes uncontrollable through its actuated joints in the position and motion singularities of forward kinematics. Therefore, the singularities of forward kinematics must be avoided. The singularity analysis also shows that the manipulator remains controllable through its actuated joints in the position and motion singularities of inverse kinematics, provided that the desired motion of the end‐effector be specified according to certain restrictive compatibility conditions. Therefore, the singularities of inverse kinematics need not be avoided, if the restricted motion of the end‐effector is acceptable or desirable for the task to be executed.
Kinematic Treatment of the Mechanisms with Simple Contact Joints (Chapters 5 and 6):In the position domain, the treatment includes the identification of the independent loops, writing the corresponding loop closure equations, and then solving them to obtain the unspecified joint variables as functions of the specified ones. The position domain treatment also includes discussions on the multiple solutions and the position singularities associated with the specified joint variables. In the velocity and acceleration domains, the treatment includes deriving the velocity and acceleration constraint equations and solving them to obtain the unspecified joint variable rates in terms of the specified ones. The velocity and acceleration analyses also include discussions on the motion singularities associated with the specified joint variables. There are several examples of such mechanisms in Chapters 5 and 6.
Kinematic Treatment of the Mechanisms with Rolling Contact Joints (Chapter 6):The rolling contact joints, i.e. the gear and cam joints, need somewhat different treatment as compared with the other simple contact joints. In particular, the mechanisms that contain cam joints with sticking friction, i.e. with the rolling‐without‐slipping property, happen to be non‐holonomic systems that have different degrees of freedom in the position and velocity domains. Therefore, the mechanisms that involve rolling contact joints with the rolling‐without‐slipping property are treated differently in the order of obtaining the kinematic solutions in the position and velocity domains. For such mechanisms, the kinematic solution is first obtained in the velocity domain and then the corresponding kinematic solution in the position domain is obtained by means of a subsequent numerical integration. The most typical samples of such mechanisms are the mechanisms that involve gear joints, because the gear joints are kinematically equivalent to the cylindrical or conical cam joints with the rolling‐without‐slipping property. A typical example of such a cam mechanism is presented in Chapter 6. The kinematic solutions of that cam mechanism in the position and velocity domains are obtained both in the cases of rolling with slipping and rolling without slipping.
Readers are encouraged and sincerely welcome to contact me at [email protected] with regard to feedback, suggestions, and questions.
Ankara, March 2019
M. Kemal Ozgoren
Acknowledgments
This book is based on the graduate courses “Advanced Dynamics” and “Principles of Robotics” that I have been teaching for a long time. Therefore, many students of these courses and several colleagues involved with related subjects have so far indicated their valuable opinions and encouraged me to write such a book. I would like to express my thanks to all of them and also to the Mechanical Engineering Department of Middle East Technical University that has provided the excellent academic medium and all the conveniences for me in developing and teaching the mentioned courses.
I would also like to express my thanks to the reviewers for their constructive comments and to all the related personnel of Wiley for their highly appreciated efforts during all the time from the initiation to the finalization of this book.
List of Commonly Used Symbols, Abbreviations, and Acronyms
Symbols Based on the Latin Alphabet
