Planar ten-bar single degree of freedom linkages have 230 valid isomers, 53 of them are kinematically indeterminate, i.e. their complete sets of instant centers cannot be obtained simply from Kennedy Theorem. This paper investigates a graphical approach, i.e. virtual cam method, to help locate the key instant centers of these kinematically indeterminate linkages, after that all the instant centers can be located by Kennedy Theorem accordingly. The criteria of application are proposed and examined carefully, the results are verified against traditional Kennedy Theorem approach and CAD modeling.

At this moment all the methods which had been proposed have extremely limited application to only several specific constructions of kinematically indeterminate linkages, i.e. their complete sets of instant centers cannot be obtained simply from Kennedy Theorem due to lack of enough four-bar loop information in their constructions. Planar single degree of freedom linkages up to ten-bar include two different types of mechanisms, i.e. pure bar linkages, such as four-, six-, eight-, and ten-bar; and geared-bar linkages, i.e. geared-five, seven, and nine-bar. The huge varieties of different types and constructions can serve as great testbeds for these methods. This research systematically investigates and modifies the graphical approach, i.e. virtual cam method, whose employment will show it to be an almost-universal method which can be compliantly applied on very wide range of kinematically indeterminate linkages. The procedures and criteria of the methodology are proposed and examined thoroughly to help locate key instant centers of all planar single degree of freedom kinematically indeterminate linkages up to ten-bar so that their complete sets of instant centers can be located successfully. We call this modified and improved technique as Virtual Cam – Hexagon Method. The results are verified carefully against traditional Kennedy Theorem approach and CAD modeling.

Kinematically indeterminate linkages are those whose complete set of instant centers cannot be obtained by Kennedy’s theorem. A linkage of this kind is often characterized as having no four-bar loop, or even if one exists, it does not lead to the finding of all other instant centers in the multiple-loop chain. This paper presents a simple graphical method for dealing with many of these linkages. While not altering the total degrees of freedom of the linkage, a virtual cam is introduced to help locate some key instant centers. This method also lends itself to applications along with Pennock’s method to achieve greater usability.

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A full nonlinear finite element P185/70R14 passenger car radial-ply tire model was developed and run on a 1.7-meter-diameter spinning test drum. The virtual tire/drum/cleat finite element model was constructed and tested using the nonlinear finite element analysis software, PAM-SHOCK. The tire model was constructed in extreme detail with three-dimensional solid, layered membrane, and beam finite elements, incorporating over 18,000 nodes and 24 different types of materials. In addition to the tire model itself, the rim was also included and rotated with the tire, with proper mass and rotational inertial effects. The FFT algorithm was applied to examine the transient response information in the frequency domain. The result showed that this P185/70R14 tire has clear peaks of 84 and 45 Hz transmissibility in the vertical and longitudinal directions. Also the paper presents the prediction of tire standing waves phenomenon, and computer animations of the standing waves phenomenon were carried out for the first time. The effects of different tire inflation pressures and tire axle loadings were investigated with respect to their influences on the formation of standing waves. The parameters adopted in this FEA tire model were validated against experimental work and showed excellent agreement.