The methodology for developing the kinematic model of selected CPR-a system as a necessity for the development of a dynamic model

Abstract

The authentic form or general form of Cable Suspended Parallel Robot type A, CPR-A mathematical model is defined. The proper definition of the system kinematic model which includes trajectory, velocity and acceleration is a prerequisite for the formulation of a dynamic model. These three components represent the basic functional criteria of the real system which is described by the corresponding geometric relations and differential equations. Kinematic model is defined for the CPR-A system via the Jacobian matrix. An adequate choice of generalized coordinates (in this paper, the internal coordinates), provides a mathematical model that illuminates the mapping of internal (resultant forces in the ropes) and external forces (acting on a camera carrier) over the Jacobian matrix on motion dynamics of each motor. Software packages AIRCAMA are formed and used for individual and comparative analysis of the CPR-A system from various aspects. The impact of changing any parameter of the system (workspace dimensions, the mass of a camera carrier, change the size and dynamics of power disturbances, the choice of control law, the reference trajectory, and the presence of singularity avoidance system and a number of other characteristics) can be analyzed through these software packages. Different examples of the CPR-A system motion are analyzed and their results are presented. The aim of this study is to define really the characteristics of CPR-A system, all this for the purpose of modernization and wider application of the same. This would be reflected in the implementation of highly-automated systems that would lead the camera precisely in space with the minimum participation of human labor. Setting and achieving this goal provide much wider possibilities for its future use. The sophisticated operation of this system can be provided only with the application of its high-fidelity mathematical model during the synthesis and analysis, which would further enable the development and application of modern control laws. Application possibilities are certainly much broader than it may be assumed at this moment, especially for sports, cultural, military or police purposes.