A Dual Number Approach to the Kinematic Analysis of Spatial Linkages With Dimensional and Geometric Tolerances

Abstract

Design robustness is somewhat connected to tolerances. In fact, the lower is the sensitivity of the kinematic function to the deviations of manufacturing process, the higher is the robustness of the design. In this investigation is described a tolerance analysis method based on dual vectors kinematic modeling of spatial linkages and on Monte Carlo simulation of the random variables. In the present analysis the hypothesis of rigid bodies is valid and only kinematic variables are considered in output. The method is applied to a Cardan joint modelled as an RCCC linkage with main dimensions considered as stochastic variables with Gaussian distribution. Dual vectors are well known in kinematic analysis and synthesis of spatial mechanisms. When compared with traditional vectorial methods, dual vectors show an enhanced capability to model misalignments among kinematic pairs axes. Although this is not the first time that dual vectors are used for the kinematic and dynamic analysis of spatial mechanisms with manufacturing errors, the present use of dual vectors to model joint clearances seems somewhat novel.

Computer-aided simulation and testing of spatial linkages with joint mechanical errors

“…For this reason the authors present a computer-aided methodology developed using the dual-algebra approach [12]. This numerical methodology [13] is very suitable for describing misalignment and backlash in kinematic pairs [14]. It allows one to write down and implement the kinematic equations in a very short form using only few parameters to describe the variety of manufacturing errors.…”

Investigation of the load and service conditions influence conditions influence on the cardan coupling operational capacity

“…Резултати су приказани дијаграмски, што омогућује да се израчуна степен искоришћења у функцији угла између оса улазног и излазног вратила. Пенестри (E.Pennestr`i) је такође истраживао утицаје угаоне брзине и угала несаосности улазног и излазног вратила на енергетске губитке [25]. Нумерички резултати су такође верификовани [26].…”