## Kinematic Analysis of Robot ManipulatorsA robot manipulator is a movable chain of links interconnected by joints. One end is fixed to the ground, and a hand or end effector that can move freely in space is attached at the other end. This book begins with an introduction to the subject of robot manipulators. Next, it describes in detail a forward and reverse analysis for serial robot arms. Most of the text focuses on closed form solution techniques applied to a broad range of manipulator geometries, from typical industrial robot designs (relatively simple geometries) to the most complicated case of seven general links serially connected by six revolute joints. A unique feature is its detailed analysis of 6R-P and 7R mechanisms. Case studies show how the techniques described in the book are used in real engineering applications. The book will be useful to both graduate students and engineers working in the field of robotics. |

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### Contents

1 Introduction | 1 |

2 Coordinate transformations | 4 |

3 Manipulator kinematics | 20 |

4 Forward kinematic analysis | 39 |

5 Reverse kinematic analysis problem statement | 44 |

6 Spherical closedloop mechanisms | 53 |

7 Displacement analysis of group 1 spatial mechanisms | 92 |

8 Group 2 spatial mechanisms | 106 |

### Other editions - View all

Kinematic Analysis of Robot Manipulators, Volume 10 Carl D. Crane, III,Joseph Duffy No preview available - 1998 |

### Common terms and phrases

angle 61 calculated values closed-loop spatial mechanism coefﬁcients constant mechanism parameters deﬁned in Eq deﬁnitions detennined determined direction cosines end effector Evaluating the scalar Expanding expression ﬁrst coordinate system ﬁxed coordinate system i j k input angle input/output equation joint angles joint axes Joint offset kinematic kinematic chain kinematic diagram linear Link length link vectors matrix modiﬁed obtained offset distance output angle position and orientation projecting the vector Puma quatemion quaternion rearranged regrouping gives reverse analysis revolute joints rotation rotation matrix scalar products secondary cosine law serial manipulator shown in Figure side of Eq simpliﬁed sine and cosine sine and sine—cosine sine—cosine laws sixth coordinate system solution sets solution tree solved speciﬁed spherical heptagon SSRMS Substituting Eqs table of direction tan-half-angle telerobotic tenns tool point transformation trigonometric identities twist angles unique corresponding value values of 61 vector loop equation vector product vector S3 written yields