Descriptive Geometric Kinematic Analysis of Clavel’s “Delta” Robot

Abstract Certain high speed industrial assembly robots share a peculiar three legged parallel architecture wherein three "hips", attached to a fixed upper base or "pelvis", actuate "thighs" connected by "knees" to "shins". Each shin is a parallelogramic four-bar linkage. "Ankles" are connected to a common end effector "foot" which executes spatial translatory motion. Inverse and direct kinematic analyses of such manipulators have simple geometric solutions reducable to intersection of line and sphere. Computation is carried out efficiently in a common fixed reference frame

Towards Integrated Type and Dimensional Synthesis of Mechanisms for Rigid Body Guidance

In this paper kinematic mapping is used to take the first steps towards development of a general algorithm combining both type and dimensional synthesis of planar mechanisms for rigid body guidance. In the present work we develop an algorithm that can size link lengths, locate joint axes, and using heuristics decide between RR-and P R-dyads that, when combined, can guide a rigid body exactly through five specified positions and orientations, i.e., the five-position Burmester problem. An example is given providing proof-of-concept

The synthesis of smooth trajectories for pick-and-place operations

A spline-based method of programming smooth trajectories for pick-and-place operations is introduced. Unlike continuous-path operations, which impose a unique Cartesian trajectory, an infinite number of smooth trajectories can be described between any given pick and its corresponding place configuration. The method begins with the mapping of the pick and the place configuration in Cartesian space into joint-coordinate space, using a general-purpose inverse kinematics package that handles singularities and redundancies. Next, a trajectory, composed of a C2-continuous, periodic cubic spline segment, is defined between the pick and the place configurations in the joint-coordinate space. It is demonstrated that C2-continuity will prevail in Cartesian space as well. The software implementing this method includes a graphics package as well as an interface to an offline programming system to realize the synthesis of the actual robot motion. Details of the procedure are illustrated with a numerical example applied to a commercial industrial robot

Solving the burmester problem using kinematic mapping

Planar kinematic mapping is applied to the five-position Burmester problem for planar four-bar mechanism synthesis. The problem formulation takes the five distinct rigid body poses directly as inputs to generate five quadratic constraint equations. The five poses are on the fourth order curve of intersection of up to four hyperboloids of one sheet in the image space. Moreover, the five poses uniquely specify these two hyperboloids. So, given five positions of any reference point on the coupler and five corresponding orientations, we get the fixed revolute centres, the link lengths, crank angles, and the locations of the coupler attachment points by solving a system of five quadratics in five variables that always factor in such a way as to give two pairs of solutions for the five variables (when they exist)