The Method of High Accuracy Calculation of Robot Trajectory for the Complex Curves

Abstract

The geometric model accuracy is crucial for product design. More complex surfaces are represented by the approximation methods. On the contrary, the approximation methods reduce the design quality. A new alternative calculation method is proposed. The new method can calculate both conical sections and more complex curves. The researcher is able to get an analytical solution and not a sequence of points with the destruction of the object semantics. The new method is based on permutation and other symmetries and should have an origin in the internal properties of the space. The classical method consists of finding transformation parameters for symmetrical conic profiles, however a new procedure for parameters of linear transformations determination was acquired by another method. The main steps of the new method are theoretically presented in the paper. Since a double result is obtained in most stages, the new calculation method is easy to verify. Geometric modeling in the AutoCAD environment is shown briefly. The new calculation method can be used for most complex curves and linear transformations. Theoretical and practical researches are required additionally.

Inverse Kinematics Data Adaptation to Non-Standard Modular Robotic Arm Consisting of Unique Rotational Modules

“…The software calculating the inverse kinematics uses the pseudoinverse computational method, also called the Moore-Penrose method and the method of dampened least squares (DLS), also called the Levenberg-Marquardt method. More information about these and other methods can be found in [16,[22][23][24]. Since other URM module configurations are contemplated for the future, or the redundant manipulator creation will be requested, it was mandatory to search for flexible solutions.…”

A New Construction of Holditch Theorem for Homothetic Motions in C p

“…In addition, some examples of the design of kinematic mechanisms were presented [31]. Then, in [32], a new alternative calculation method of high accuracy calculation of robot trajectory for the complex curves was proposed. On the other hand, the similarity method has found a place in science for several centuries.…”