روش مبتنی بر نیروی ساده برای خطی سازی و تجزیه و تحلیل حساسیت سیستم دستکاری پیچیده

In this paper a method is proposed to efficiently linearize the geometry of complex multibody systems by exploiting the kinetostatic dualism, i.e. formulating the linearization in terms of the force transmission. In this setting, an algorithm is introduced by which one can perform the linearization of the transmission behavior from any number of geometric parameters to the motion of a six-degree-of-freedom end-effector by applying six unit loads to the end-effector and determining internal forces. Moreover, applications in first-order error analysis, calculation of the stiffness matrix, and calibration of manipulators are proposed. Examples of both serial and fully parallel manipulators are presented.

The analysis of manufacturing and assembly errors of manipulators is a topic that is highly relevant for practical applications because the magnitude of these errors is directly coupled to the total cost of production of the manipulator. In this setting, there exist intensive studies on how to estimate the error of certain moving points, e.g. the tool center point, in terms of the errors in the components of the mechanism [1], [2], [3], [4] and [5], as well as how to allocate cost-optimal tolerances to a mechanism [6] and [7]. In this paper, a new approach to estimate the first-order influence of geometric errors on target quantities is suggested in which linearization is performed by considering the force transmission of the manipulator. This enables one to obtain a comprehensive model of linearized geometric sensitivities at a low computational cost.

In this work, a general method is proposed to compute the linearization of the transmission behavior from geometric parameters to the end-effector motion of a manipulator. It is shown that by applying the force transmission method, one can perform a sensitivity analysis with respect to all geometric parameters, both for serial manipulators and for mechanisms involving closed kinematic loops. Especially in cases where no closed-form solution for the direct kinematics is available, the force-based approach provides an efficient procedure for obtaining the linearized equations. The method is applicable to standard kinematical models of the manipulator and permits to study parameters that would be canceled in the closure conditions. Based on the linearization of the manipulator, methods for error analysis, calculation of the geometric error stiffness matrix, and calibration are provided. It is shown that the algorithm provides a good numerical performance and that it can be applied to practical examples.