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Introduction to Robotics Chapter 3. Differential Motions and Velocities

Introduction to Robotics Chapter 3. Differential Motions and Velocities. School of Electrical and Electronic Engineering Chung-Ang University Ubiquitous Robot and Intelligent Information System Lab. Prof. Kwee-Bo Sim. 3.2 Differential Relationships.

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Introduction to Robotics Chapter 3. Differential Motions and Velocities

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  1. Introduction to RoboticsChapter 3. Differential Motions and Velocities School of Electrical and Electronic Engineering Chung-Ang University Ubiquitous Robot and Intelligent Information System Lab. Prof. Kwee-Bo Sim

  2. 3.2 Differential Relationships Fig. 3.1 (a) A two d.o.f. Planar mechanism and (b)velocity diagram 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  3. 3.3 Jacobian 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  4. 3.4 Differential Motions of a Frame Fig.3.2 (a)Different motions of a frame and (b)different motions of a frame as related to the differential motions of a robot 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  5. 3.4 Differential Motions of a Frame 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  6. 3.5 Interpretation of the Differential change 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  7. 3.6 Differential changebetween frames 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  8. 3.6 Differential changebetween frames 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  9. 3.6 Differential changebetween frames 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  10. 3.7 Differential Motions of a Robot and Its Hand Frame 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  11. Manipulator Jacobian 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  12. Manipulator Jacobian • Manipulator Jacobian relates the velocity of the joints in the joint space to the velocity of the hand in Cartesian space. • The inverse jacobian relates the velocity of the hand in Cartesian space to the joint velocities. • The number of columns in a Jacobian is determined by the number of joints in the manipulator, that is, the degree of mobility in the joint space required. • If there are more columns than rows the manipulator is redundant. That is, the number of degrees of mobility of the manipulator is greater than the number of degrees of freedom required by the task, and we have multiple inverse solutions. • In this case, we can take advantage of these to avoid collisions, or some joints can be locked to produce a square matrix. • For many manipulators, the Jacobian will not be square. In order to invert a non-square Jacobian, we define some of the pseudo inverse . 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  13. 3.8 Calculation of the Jacobian 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

  14. 3.10 Inverse Jacobian Fig 3.3 Reference frames for the simple six-degree-of-freedom articulate robot 중앙대학교 전자전기공학부 인공생명 및 지능정보시스템연구실

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