Serial robots
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This Chapter describes the common physical properties and the mathematical coordinate representations and algorithms, to work with (i) the position, velocity and acceleration kinematics of serial robots, and (ii) their dynamics.
The position and orientation of a robot's end-effector are derived from the joint positions by means of a geometric model of the robot arm. For serial robots, the mapping from joint positions to end-effector pose is “easy”, while the inverse mapping is, in general, more difficult. Therefore, most industrial robots have special designs that reduce the complexity of the inverse mapping. Many popular designs involve a spherical wrist.
The key topics discussed in this Chapter are:
- Forward and inverse kinematics, for position, velocity and acceleration. Closed-form as well as numerical techniques are discussed.
- Forward and inverse statics, i.e., the transformation of forces between joint space and end-effector space.
- The properties of singularities and redundancies, and the common mathematical algorithms to deal with them.
- The influence of contact constraints on the end-effector.
- The dynamics of chains of rigid bodies and ideal links, in the form of iterative numerical algorithms, as well as in analytical form derived from variational principles.