Relationship between numbers of point forces and sensing elements in flexible tactile sensors

Tactile sensor with good flexibility is a promising candidate for artificial skin of intelligent robots. Some specific structures and models have been proposed to realize sensing of 3-demensional tactile forces. Due to the natural couple properties of these sensor models, decoupling has become an obstacle on the road to practical sensors. In this paper, we start from an elastic mechanics model which could approximately characterize the relationship between 3-dimensional forces applied on the surface of the sensor and its deformation. Further analysis shows that the deformations caused by several forces could be treated separately in the point force applied scenario. According to this analysis, we derive an exact relationship between the numbers of the sensing elements and the applied forces. We confirm this relationship by numerically computing the Jacobian matrix and investigating the singular values of it.