Abstract
The study of the kinematics and dynamics of robot mechanisms has employed different frameworks, such as vector calculus, quaternion algebra, or linear algebra; the last is used most often. However, in these frameworks, handling the kinematics and dynamics involving only points and lines is very complicated. In previous chapter, the motor algebra was used to treat the kinematics of robot manipulators using the points, lines, and planes. We also used the conformal geometric algebra which includes for the representation also circles and spheres. The use of additional geometric entities helps even more to reduce the representation and computational difficulties.
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Notes
- 1.
In mathematics, two differentiable functions f and g are related via a Legrende transformation if each of their first derivatives is inverse function of the other, i.e., \(Df=(Dg)^{-1}\).
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Bayro-Corrochano, E. (2020). Robot Dynamics. In: Geometric Algebra Applications Vol. II. Springer, Cham. https://doi.org/10.1007/978-3-030-34978-3_11
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DOI: https://doi.org/10.1007/978-3-030-34978-3_11
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