Abstract
Kinematic geometry is the fundamentals in the modeling and programming of a robot. In this chapter, rigid body kinematics, purely geometrical aspects of individual positions and of continuous motions of rigid bodies, are studied. We firstly introduce some basic material, e.g., the homogeneous transformation, rotation matrix, and the representations of the points, vectors and transformation between them. Several parallel PnP robots with different mobilities are illustrated as examples. The kinematic workspace envelope, namely, the set of positions that a robot can reach, is studied with either numerical searching or geometric approaches.
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Notes
- 1.
The inherent coordinate frame attached to the body coincides with the reference coordinate frame.
- 2.
The two frames are not coincident but with all the coordinate axes parallel.
- 3.
Throughout this book, \(\mathbf {I}_N\) stands for a N-dimensional identity matrix, and \(\mathbf {O}_N\) stands for a N-dimensional null matrix, while \(\mathbf {q}_n\) stands for a n-dimensional column vector.
- 4.
Capital CPM stands for cross-product matrix, differing from cpm (cycles per minute) in lowercase.
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© 2021 Huazhong University of Science and Technology Press, Wuhan and Springer Nature Singapore Pte Ltd.
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Wu, G., Shen, H. (2021). Kinematic Geometry of the PnP Robots. In: Parallel PnP Robots. Research on Intelligent Manufacturing. Springer, Singapore. https://doi.org/10.1007/978-981-15-6671-4_2
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DOI: https://doi.org/10.1007/978-981-15-6671-4_2
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-6670-7
Online ISBN: 978-981-15-6671-4
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