Determination of necessary geometric parameters of tripod robot workspace, taking into account zones of singularity

Abstract

Abstract-The article considers the problem of providing the necessary geometric parameters of the workspace of a flat robot with 3 degrees of freedom. The influence of the geometric parameters of the robot mechanism configuration (drive mechanisms rod lengths and working platform parameters) as well as the working platform angle of rotation on the dimensions of the workspace was investigated. Special provisions (singularity zones) of the mechanism should be excluded from the robot workspace. The mechanism under investigation has singularities of the second type. Increasing angle φ that decreases the size of the workspace, but increases radius θ of the circle, on which the points of singularity are located, is shown. Thus, it is necessary to limit the swing angle range and expand the variation range of the lengths of the rods' change to ensure the necessary size of the workspace mechanism. For the given dimensions of the workspace (based on the requirements of the technological process), the task of determining the geometric parameters of the robot mechanism configuration is solved. Mathematical modeling is performed. The results of computational experiments are presented.

Synthesis of Parallel Robots Optimal Motion Trajectory Planning Algorithms

“…5. The values of the output coordinates (x, y, φ) are determined on the basis of neural network functions [9], providing the solution of the direct kinematic analysis problem. 6.…”

“…Optimization of the positioning trajectory is a complex scientific task of the mechanism output link safe motion trajectory C 0 C 1 C K determination on a uniform discrete grid ensuring a minimum of the total positioning time t. Safe motion is the movement at a distance not less than the specified from the boundaries of the working area and mechanism singularity zones [2], determined by its geometric characteristics [9,14] and also from the surface of the workpiece. The described limitations can be specified both in the form of corresponding inequalities and in the form of an array of discrete points forbidden or allowed to be included in the trajectory.…”

“…The described limitations can be specified both in the form of corresponding inequalities and in the form of an array of discrete points forbidden or allowed to be included in the trajectory. As shown in [14] and [9], the output coordinates x, y, φ (Fig. 2) of this mechanism (working space) are limited by the range of permissible lengths of the drive links and area where the Jacobian sign is constant.…”