Devising a Method to Analyze the Current State of the Manipulator Workspace

This paper has proposed a program analysis method over the current state of the workspace of an anthropomorphic manipulator using the Mathcad software application package (USA). The analysis of the manipulator workspace helped solve the following sub-tasks: to calculate the limits of the grip reach, to determine the presence of "dead zones" within the manipulator workspace, to build the boundaries of the manipulator workspace. A kinematic scheme of the manipulator typically provides for at least five degrees of mobility, which is why in the three-dimensional Cartesian coordinate system the work zone boundaries represent the surfaces of a complex geometric shape. The author-devised method makes it possible to construct the projections of the boundaries of the manipulator's work zone onto the coordinate planes in the frame of reference associated with the base of the robot.

Using Mathcad's built-in features makes it possible to effectively solve the above sub-tasks without wasting time developing specialized software. The Mathcad software application package provides for the possibility of a symbolic solution to the first problem of the kinematics of an industrial robot, that is, the program generates analytical dependences of the coordinates for special point P (pole) of the grip on the trigonometrical functions of the generalized coordinates. The resulting analytical dependences are used for kinematic and dynamic analysis of the manipulator.

Special features in constructing mathematical models when using the Mathcad software application package have been revealed. Simulating the manipulator movement taking into consideration constraints for kinematic pairs, the drives' power, as well as friction factors, makes it possible to optimize the parameters of the manipulator kinematic scheme.

An example of the analysis of the working space of an anthropomorphic manipulator with five degrees of mobility has been considered.

The reported results could be used during the design, implementation, modernization, and operation of manipulators.