Abstract
The purpose of this chapter is to introduce you to the kinematics of limbs. Kinematics is the study of movements without regard to the forces and torques that produce them. In essence, it is the fundamental description of the articulations and motions of which a limb is capable. This chapter serves as the foundation upon which we can build a common conceptual language, and begin to discuss limb function in the context of mechanics.
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Notes
- 1.
In biological systems, joint kinematics arise from the interaction of the contact of bony articulating surfaces held by ligamentous structures. A joint is, therefore, a complex system whose kinematics can be load dependent [1].
- 2.
We use the term torque-driven instead of joint-driven because this is more common in the robotics literature.
- 3.
In robotics, the term manipulator is used synonymously with robot, robotic arm, robotic limb, or any other mechanism that is actuated and controlled.
- 4.
Actuator is the generic engineering term for a motor or some other device that produces forces or mechanical work.
- 5.
A note about typesetting conventions set forth in Appendix A. Capital letters as superscripts or subscripts (italicized or not) like M or N indicate extremes of ranges. Thus the endpoint of a limb is assigned frame N, and dimensionality of a vector or matrix are \(\mathbf {v} \in \mathbb {R}^N\) or \(A \in \mathbb {R}^{M \times N}\), respectively. Indices that are lowercase italicized letters like n, i, or j signify a number within a range. The letter M need not stand for muscles, or n for an intermediate frame of reference. They are simply letters to indicate dimensions and indices, and change with the context of the material. Vectors are lowercase letters typeset as \(\mathbf {v}\), which can be also specified to be expressed in a given frame of reference, say frame 0, as \(\mathbf {v}_{0}\). Or if the start and end of a vector are specified, it will be typeset as \(\mathbf {p}_{0,N}\). Matrices are written as italicized upper case letters, such at the matrix T, which can also carry subscripts and superscripts depending on their meaning like \(T_{\textit{base}}^{\textit{endpoint}}\). I use lowercase italics for general scalars (i.e., numbers).
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Valero-Cuevas, F.J. (2016). Limb Kinematics. In: Fundamentals of Neuromechanics. Biosystems & Biorobotics, vol 8. Springer, London. https://doi.org/10.1007/978-1-4471-6747-1_2
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DOI: https://doi.org/10.1007/978-1-4471-6747-1_2
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