A new equilibrator design approach based on system potential energy functions is presented. This approach was used to discover a group of spring equilibrators which perfectly balance a rotatable rigid link at every orientation angle through 360 deg of link rotation. Springs are connected between a rotatable link and ground, where one end of each spring is connected to the rigid link and the other end of each spring is connected to ground. The rigid link is connected to ground by a pin joint and is free to rotate about that joint. The conditions for existence and the design equations for all equilibrators which fall into this category are developed and presented. Three designs appear to offer unique advantages over the infinite number of design options available.
A probabilistic model and methods to determine the means and variances of the velocity and acceleration within stochastically-defined planar pin jointed kinematic chains are presented. The presented model considers the effect of tolerances on link length and radial clearance and uncertainty of pin location as a net effect on the link’s effective length. The determination of the mean values and variances of the output variables requires the calculation of sensitivities of secondary variables with respect to the random variables. It is shown that this computation is straightforward and can be accomplished by a conventional kinematic analysis package. Thus, the concepts of tolerance and clearance have been captured by the model and analysis. The only input data is the nominal linkage model and statistical information. The “effective link length” model is shown to be applicable to both analytical solution and Monte Carlo simulation. The results from both methods are compared. This paper solves the higher-order kinematics problem for the probabilistic design analysis of stochastically defined mechanisms.
When a multi-body system collides with a single body or with another multi-body system, impact dynamics with friction should be considered. This paper presents a general computer oriented analysis of impact dynamics incorporating friction. The presence of friction between sliding contacts during the impact makes the problem difficult since the events such as reverse sliding or sticking, which may occur at different times throughout the impact, must be determined. The boundary representations of the bodies are used to solve for the velocities at the points of contact. Using this information and a classification of the modes of impact, the frictional impact with sliding contact problem is solved. Using a high speed video camera, the resulting computer strategy is experimentally verified. Simulation and experimental results agree.
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