Kinematic Analysis of the Human Thumb with Foldable Palm

Abstract

There have been numerous attempts to develop anthropomorphic robotic hands with varying levels of dexterous capabilities. However, these robotic hands often suffer from a lack of comprehensive understanding of the musculoskeletal behavior of the human thumb with integrated foldable palm. This paper proposes a novel kinematic model to analyze the importance of thumb-palm embodiment in grasping objects. The model is validated using human demonstrations for five precision grasp types across five human subjects. The model is used to find whether there are any co-activations among the thumb joint angles and muskuloskeletal parameters of the palm. In this paper we show that there are certain pairs of joints that show stronger linear relationships in the torque space than in joint angle space. These observations provide useful design guidelines to reduce control complexity in anthropomorphic robotic thumbs.

A APPENDIX: The Transformation Matrices for the Kinematic Model

$$\begin{aligned} ^{0} _{1} T = \left[ \begin{array}{cccc} cos(90 + \gamma _{1}) &{} 0 &{} sin(90 + \gamma _{1}) &{} 0 \\ 0 &{} 1 &{} 0 &{} 0 \\ -sin(90 + \gamma _{1}) &{} 0 &{} cos(90 + \gamma _{1}) &{} 0 \\ 0 &{} 0 &{} 0 &{} 1 \end{array} \right] ~~~ ^{1} _{2} T = \left[ \begin{array}{cccc} cos (\theta _1) &{} -sin(\theta _1) &{} 0 &{} l_{1} \\ sin(\theta _1) &{} cos(\theta _1) &{} 0 &{} 0 \\ 0 &{} 0 &{} 1 &{} l_2 \\ 0 &{} 0 &{} 0 &{} 1 \end{array} \right] \end{aligned}$$

$$\begin{aligned} ^{2} _{3} T = \left[ \begin{array}{cccc} cos (\theta _2) &{} -sin(\theta _2) &{} 0 &{} 0 \\ 0 &{} 0 &{} -1 &{} -l_3 \\ sin(\theta _2) &{} cos(\theta _2) &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 1 \end{array} \right] ~~~ ^{3} _{4} T = \left[ \begin{array}{cccc} cos (\theta _3) &{} -sin(\theta _3) &{} 0 &{} 0 \\ 0 &{} 0 &{} 1 &{} 0 \\ -sin(\theta _3) &{} -cos(\theta _3) &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 1 \end{array} \right] \end{aligned}$$

$$\begin{aligned} ^{4} _{5} T = \left[ \begin{array}{cccc} cos (\theta _4) &{} -sin(\theta _4) &{} 0 &{} 0 \\ 0 &{} 0 &{} -1 &{} 0 \\ sin(\theta _4) &{} cos(\theta _4) &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 1 \end{array} \right] ~~~ ^{5} _{6} T = \left[ \begin{array}{cccc} cos (\theta _5) &{} -sin(\theta _5) &{} 0 &{} l_4 \\ 0 &{} 0 &{} -1 &{} 0 \\ sin(\theta _5) &{} cos (\theta _5) &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 1 \end{array} \right] \end{aligned}$$

$$\begin{aligned} ^{6} _{7} T = \left[ \begin{array}{cccc} cos (\theta _6) &{} -sin(\theta _6) &{} 0 &{} 0 \\ 0 &{} 0 &{} 1 &{} 0 \\ -sin(\theta _6) &{} -cos (\theta _6) &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 1 \end{array} \right] ~~~ ^{7} _{8} T = \left[ \begin{array}{cccc} cos (\theta _7) &{} -sin(\theta _7) &{} 0 &{} l_{5} \\ 0 &{} 0 &{} -1 &{} 0 \\ sin(\theta _7) &{} cos (\theta _7) &{} 0 &{} 0 \\ 0 &{} 0 &{} 0 &{} 1 \end{array} \right] ~~~ ^{8} _{9} T = \left[ \begin{array}{cccc} 1 &{} 0 &{} 0 &{} l_{6} \\ 0 &{} 1 &{} 0 &{} 0 \\ 0 &{} 0 &{} 1 &{} 0 \\ 0 &{} 0 &{} 0 &{} 1 \end{array} \right] \end{aligned}$$