The Determination of the Probabilistic Properties of Velocities and Accelerations in Kinematic Chains With Uncertainty

Lee, S. J.; Gilmore, Brian

doi:10.1115/1.2912755

Cited by 86 publications

(39 citation statements)

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“…Lee and Gilmore [16] subsequently generalized that method to incorporate the uncertainties associated with pin locations and variations in link length. With a generalized vector loopbased model to represent small kinematic adjustments, Chase et al [17] presented the direct linearization method (DLM) for the tolerance analysis of twodimensional mechanisms.…”

Section: Introductionmentioning

confidence: 98%

Effect of manufacturing tolerances on dynamic equilibria of multibody systems undergoing prescribed rotational motion

2008

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A general formulation is developed for the tolerance analysis of dynamic equilibria in a multibody system undergoing prescribed rotational motion, with applications including robots, spacecraft, propulsion and power generation systems, and sensors and actuators. In a state of dynamic equilibrium, a subset of the generalized coordinates assumes constant values while the remaining coordinates vary and respond in time. Manufacturing tolerances can be mathematically represented by probabilistic distributions or statistical variables through either an analytical approach or a Monte Carlo simulation. In the present tolerance work, the tolerances of design parameters including lengths, stiffnesses, inertias, and attachment positions are examined. In order to analytically calculate the statistical response of the dynamic equilibrium positions to such tolerances, the first-order sensitivities of the equilibria with respect to parameters are calculated. To illustrate the method's accuracy and computational efficiency, two numerical examples are considered, and the statistical results obtained analytically for the equilibria are compared with those calculated through Monte Carlo simulation. In some cases, an equilibrium configuration can have an operating condition for which the response has zero standard deviation to perturbations of a design parameter. That condition can be a useful design point to the extent that typical manufacturing tolerances or other sources of variation would have no effect on the dynamic equilibrium configuration.

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Section: Introductionmentioning

confidence: 98%

Effect of manufacturing tolerances on dynamic equilibria of multibody systems undergoing prescribed rotational motion

2008

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“…In Ref. [3], the probability characteristics of the speed and the acceleration for the mechanism kinematic chain were studied;…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis of kinematic accuracy for the elastic slider-crank mechanism

Chen

Yao-fei

Chijiang

et al. 2007

Front. Mech. Eng. China

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in Refs. [4][5], the accuracy analysis based on the probability of the spatial linkage mechanism with one revolute pair and three cylindric pairs and the linkage mechanism with clearances were made respectively. In Refs. [6][7][8], the optimal designs of the planar four-bar linkage mechanism, the linkage mechanism with clearances and the compliant mechanism were made respectively. However, the dynamic accuracy problem is far more complex than the static accuracy problem, therefore, the theory and method on the dynamic accuracy of the mechanism are still not perfect, and the papers on this are relatively few. In this paper, the static and dynamic output kinematic errors of the elastic slider-crank mechanism are analyzed and synthesized. Based on the above, the reliability model of the output kinematic accuracy of the mechanism is built. Through an example, a study of the influencing factors on the reliability of the output kinematic accuracy of the mechanism is made.

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“…Under normal circumstances, the errors of manufacture and measurement are normally distributed, it can be seen that the actual gear rack installation and operation position should be in the range of deviation from normal distribution [21,22]. Based on the assumption that the error distribution of mechanical manufacturing is normal distribution, two important assumptions are put forward:…”

Section: Probabilistic Analysis Of Gear Rack Motionmentioning

confidence: 99%

Research on Time-Variant Wear Reliability of Gear Rack

Li¹,

Wang²,

Liu³

et al. 2017

IJMEA

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Abstract:In this paper, a gear rack of a ship lift is taken as an example. This paper presents a method for analyzing the reliability of gear and rack movement under the influence of time-varying wear. The example of large modulus gear rack mechanism for ship lift is verified. Through the wear state of rack and pinion, the time dependent reliability equation of kinematic pair is established with the consideration of the original dimension error, gap error and wear effect. Based on the Archard wear model, the hardness and other factors under the influence of time variation are analyzed and the new kinematic pair model is established. Finally, the Matlab software is used to simulate the wear process of the rack and pinion. The influence degree of the above factors on the motion reliability of mechanism is analyzed. The results of simulation and analysis show that the method is more accurate and suitable for engineering application. It provides an important reference for the life prediction of gear rack and the development of maintenance and maintenance outline.

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The Determination of the Probabilistic Properties of Velocities and Accelerations in Kinematic Chains With Uncertainty

Cited by 86 publications

References 0 publications

Effect of manufacturing tolerances on dynamic equilibria of multibody systems undergoing prescribed rotational motion

Effect of manufacturing tolerances on dynamic equilibria of multibody systems undergoing prescribed rotational motion

Reliability analysis of kinematic accuracy for the elastic slider-crank mechanism

Research on Time-Variant Wear Reliability of Gear Rack

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