Dual number algebra is a powerful mathematical tool for the kinematic and dynamic analysis of spatial mechanisms. With the purpose of exploiting new applications, in this paper are presented the dual version of some classical linear algebra algorithms. These algorithms have been tested for the position analysis of the RCCC mechanism and computational improvements over existing methods obtained
SUMMARYTolerance allocation influences production costs in a big way. For this reason it is very important to have an accurate study about the effects of manufacturing errors on the functioning and performances of linkages. In this paper, the authors present a computer-aided methodology based on a 3D geometrical approach using the dual-algebra fundamentals. The purpose is to give an useful tool which can be integrated into CAD software in order to evaluate the performances of spatial mechanisms with mechanical errors. The proposed methodology has been validated by means of experimental tests on a Cardan joint mechanism with clearances, misalignments and dimensional errors.
The comfort assessment for car occupants is not an easy task to achieve. It [3,4]. In this paper the influence of the anthropometric features (height and weight) and the inclination of the backrest on the VDV has been investigated. The code is an useful tool for predicting at the seat design level the vibrational discomfort.
The model of a three dimensional journal bearing with hydrodynamic lubrication is herein presented. This model is suitable for embodiment into the equations of spatial multibody systems. Both rotational and squeeze effects together with tilting effect have been taken into account. Moreover a simplified model of friction has been also reported. The proposed methodology has been applied to an example concerning an unbalanced rotor supported by two journal bearings.
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.
In this paper a simulation of the cam actuator of a robotized gearbox is presented. The actuator is a barrel cam which moves a pin according to a prescribed motion law. The model of contact, between cam and follower, is based on a finite elements approach of the theory of beam on continuous elastic foundation, modified by the authors to include the effect of shear on the deformation and dynamic effects. The foundation modulus is computed using Hertz theory taking also into account the change of principal curvature values during the relative motion between cam and follower. This model has been embodied in a complete gear shifting simulation in order to compare the effects on contact forces, wear actions and shifting time of different cam profiles.
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