• Kenneth J. WaldronEmail author
  • James Schmiedeler
Part of the Springer Handbooks book series (SHB)


Kinematics pertains to the motion of bodies in a robotic mechanism without regard to the forces/torques that cause the motion. Since robotic mechanisms are by their very essence designed for motion, kinematics is the most fundamental aspect of robot design, analysis, control, and simulation. The robotics community has focused on efficiently applying different representations of position and orientation and their derivatives with respect to time to solve foundational kinematics problems.

This chapter will present the most useful representations of the position and orientation of a body in space, the kinematics of the joints most commonly found in robotic mechanisms, and a convenient convention for representing the geometry of robotic mechanisms. These representational tools will be applied to compute the workspace, the forward and inverse kinematics, the forward and inverse instantaneous kinematics, and the static wrench transmission of a robotic mechanism. For brevity, the focus will be on algorithms applicable to open-chain mechanisms.

The goal of this chapter is to provide the reader with general tools in tabulated form and a broader overview of algorithms that can be applied together to solve kinematics problems pertaining to a particular robotic mechanism.






cylindrical joint


degree of freedom


helical joint


prismatic joint


revolute joint


universal joint


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Centre of Mechatronics and Intelligent SystemsUniversity of Technology SydneyUltimoAustralia
  2. 2.Department of Aerospace and Mechanical EngineeringUniversity of Notre DameNotre DameUSA

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