Singular surfaces and cusps in symmetric planar 3-RPR manipulators

Abstract

This paper deals with the problem of estimating the position of tactile elements (i.e. taxels) that are mounted on a robot body part. This problem arises with the adoption of tactile systems with a large number of sensors, and it is particularly critical in those cases in which the system is made of flexible material that is deployed on a curved surface. In this scenario the location of each taxel is partially unknown and difficult to determine manually. Placing the device is in fact an inaccurate procedure that is affected by displacements in both position and orientation. Our approach is based on the idea that it is possible to automatically infer the position of the taxels by measuring the interaction forces exchanged between the sensorized part and the environment. The location of the contact is estimated through force/torque (F/T) measures gathered by a sensor mounted on the kinematic chain of the robot. Our method requires few hypotheses and can be effectively implemented on a real platform, as demonstrated by the experiments with the iCub humanoid robot.

Asymptotic Singularities of Planar Parallel 3-RPR Manipulators

“…This is the case for the "symmetric" manipulators [15]: in this case the inner branch of the asymptotic singularity curve is reduced to a point. We plan to study the stable perturbations of such manipulators in a future work.…”

Perturbation of Symmetric 3-RPR Manipulators and Asymptotic Singularities

“…Symmetric 3-RPR manipulators (those for which the platform triangle is congruent to the base triangle by an orientation-reversing isometry) have special kinematic properties (see [3]). Since these manipulators are not generic, the question arises of how a small perturbation of the architecture will influence the kinematic properties of the manipulator.…”

“…This branch is a deltoid with three cusps (cf [3]). The image of this deltoid in the plane with coordinates (ℓ 2 , ℓ 3 ) tends to the point (0, 0) (the degenerate inner branch of the asymptotic singularity curve) as r 1 tends to infinity.…”