Abstract
The recent development of highly anthropomorphic avatars in computer graphics has emphasized the importance of accurate hand kinematic models. Although kinematic methods derived from robotics have recently been applied to the modeling of hands, we consider that original/new and relevant results can be brought into play with the use of more advanced applications of robotic techniques to human hand kinematic modeling. Our chapter analyses some of these questions both in the non-differential and differential fields. More specifically, we study how to integrate the peculiar natural digit movement constraints into robotics-based inverse kinematic modeling. As a result, we propose an original approach based on an interpretation of each joint dynamic constraint as a linear joint synergy. This leads to defining the considered digit as a serial chain kinematically redundant in position and reducing the dimension of its joint space by associated joint synergies. The method is applied to the Cartesian positioning simulation of a 4 d.o.f. index model; a comparison with a Jacobian pseudo-inverse-based approach emphasizes its relevance.
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Notes
- 1.
Note that the ‘dynamic’ term in the ‘hand dynamic constraints’ expression has a kinematic meaning as it will appear in the chapter.
- 2.
Throughout this chapter we use the following abbreviations: the five metacarpals are noted M1 to M5 where the number refers to the digit number (from 1 for the thumb to 5 for the little finger); the proximal, middle and distal phalanges are, respectively, noted PP, MP and DP; CMC stands for carpometacarpal (we will use it also for the thumb as equivalent to TM for trapezometacarpal), MCP for metacarpophalangeal, IP for interphalangeal, DIP for distal interphalangeal and PIP for proximal interphalangeal.
- 3.
A definition of a finger “natural posture” by the linear relationship between joint variables θ 1 and θ 2: \( \alpha \theta _1 + \beta \theta _2 + \gamma = 0 \) where α, β, γ are constants, can be found in [26]. In comparison with this study, our aims are to propose a general joint synergy linear relationship integrated into a Jacobian-based differential approach.
- 4.
This 5 d.o.f. model can if necessary be completed by a CMC pronation movement, and the observed fact that ‘flexion and pronation [are] linearly coupled at the CMC joint during opposition’ [11] (page 506) can be expressed by a supplementary relationship such as – with three new constants \(c^{\prime\prime}_1 \), \(c^{\prime\prime}_2 \)and \(b^{\prime\prime}\) : \(c^{\prime\prime}_1 \theta _{CMC}^{flex} {\rm{ }} + {\rm{ }}c^{\prime\prime}_2 \theta _{CMC}^{pron} {\rm{ }} = {\rm{ }}b^{\prime\prime}\). The three chosen control variables are the same in this 6 d.o.f. thumb model with three linear joint relationships.
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Tondu, B. (2009). Human Hand Kinematic Modeling Based on Robotic Concepts for Digit Animation with Dynamic Constraints. In: Magnenat-Thalmann, N., Zhang, J., Feng, D. (eds) Recent Advances in the 3D Physiological Human. Springer, London. https://doi.org/10.1007/978-1-84882-565-9_4
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