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Robotic manipulators are widely used in industry. They are simpler than mobile robots in that they perform tasks in a fixed and known environment. They are more complex than mobile robots because they move in the three spatial dimensions and in the three dimensions of rotation. Using a simplified planar model of a robotic arm, the two central problems of manipulators are presented. Forward kinematics asks where the end effector of the arm will be following a sequence of rotations of the joints of the arm. Inverse kinematics asks what rotations of the joints will bring the end effector to a specified position. A rotation of a robotic manipulator is described by a rotation matrix whose elements are trigonometric functions of the angle of rotation. The rotation matrix for a planar rotation is derived followed by an overview of three-dimensional rotations.
Correll, N.: Introduction to Autonomous Robots. CreateSpace (2014). https://github.com/correll/Introduction-to-Autonomous-Robots/releases/download/v1.9/book.pdf
Craig, J.J.: Introduction to Robotics: Mechanics and Control, 3rd edn. Pearson, Boston (2005)
Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control. Wiley, New York (2005)
Vince, J.: Quaternions for Computer Graphics. Springer, Berlin (2011)
- Kinematics of a Robotic Manipulator
- Chapter 16