Kinematics of General Spatial Mechanical Systems. M. Kemal Ozgoren

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

Acceleration of an implied point (in a general use)Acceleration of a point P with respect to an implied reference frameAcceleration of a point P with respect to a reference frame ; b_kEffective length of between and along A rigid body denoted by the index a and represented by the frame Orientation matrix of an implied body or frame (in a general use)Orientation matrix of the end‐effector () with respect to the base frame; CTM that transforms components from to ; Orientation matrix of with respect to ; Orientation matrix of with respect to Orientation matrix of with respect to ; A general column matrix; A general row matrix, i.e. the transpose of Skew symmetric matrix generated from ; D_aVector differentiator with respect to ; d_kConstant offset of with respect to if is revoluted_mTip point offset; d_m = RP = O_{m − 1}O_mEElbow point of a manipulatorExponential form of Exponential form of Kinematic element of that mates with