On the kinematic constraint surfaces of general three-legged planar robot platforms

The variants of general three-legged planar robot platforms are enumerated and classified. Constraint surfaces corresponding to individual platform legs in the kinematic mapping image space are classified and parametrized. The parametric equations are free from representational singularities. The entire set consists of hyperboloids of one sheet and hyperbolic paraboloids. This result corrects an oversight in the body of literature. These surfaces have important applications to the kinematic analysis of planar three-legged robot platforms, hence appropriate attention should be given to their classification

Solving the forward kinematics of a planar three-legged platform with holonomic higher pairs

A practical solution procedure for the forward kinematics problem of a fully-parallel planar three-legged platform with holonomic higher pairs is presented. Kinematic mapping is used to represent distinct planar displacements of the end-effector as discrete points in a three dimensional image space. Separate motions of each leg trace skew hyperholoids of one sheet in this space. Therefore, points of intersection of the three hyperholoids represent solutions to the forward kinematics problem. This reduces the problem to solving three simultaneous quadratics. Applications of the platform are discussed and an illustrative numerical example is given

Extreme distance to a spatial circle

Determination of shortest distances in the three dimensional task space of robots is pertinent to pick-and-place operations, collision avoidance, and for impact prediction in dynamic simulation. The conventional approach is to find perpendicular distances between planar patches approximating body surfaces. In contrast, this paper treats four variants of shortest distance computations wherein one or both elements are circular edges. These three dimensional cases include circle and point, circle and plane, circle and line and two non coplanar circles. Solutions to these four fundamental problems are developed with elementary geometry. Examples are presented, and the closed form algebraic solutions are verified with descriptive geometric constructions

Singular configurations of wrist-partitioned 6R serial robots: A geometric perspective for users

In this paper the singular configurations of wrist-partitioned 6R serial robots in general, and the KUKA KR-15/2 industrial robot in particular, are analytically described and classified. While the results are not new, the insight provided by the geometric analysis for users of such robots is. Examining the problem in the joint axis parameter space, it is shown that when the end-effector reference point is taken to be the wrist centre the determinant of the associated Jacobian matrix splits into four factors, three of which can vanish. Two of the three potentially vanishing factors give a complete description of the positioning singularities and the remaining one a complete description of the orientation singularities, in turn providing a classification scheme

Sphérique et Six Couples Rotöides: une Perspective

In this paper the singular configurations of wrist-partitioned 6R serial robots in general, and the KUKA KR-15/2 industrial robot in particular, are analytically described and classified. While the results are not new, the insight provided by the geometric analysis for users of such robots is. Examining the problem in the joint axis parameter space, it is shown that when the end-effector reference point is taken to be the wrist centre the determinant of the associated Jacobian matrix splits into four factors, three of which can vanish. Two of the three potentially vanishing factors give a complete description of the positioning singularities and the remaining one a complete description of the orientation singularities, in turn providing a classification scheme