No abstract

No abstract

A novel method for kinematic analysis of parallel-axes epicyclic gear trains is presented, called the incidence and transfer method, which uses the incidence matrices associated with the edge-oriented graph associated to the mechanism and the transfer joints (teeth contact joints). Relative to such joints, a set of independent equations can be generated for calculating the angular positions, velocities, and accelerations. Complete kinematic equations are obtained in matrix form using a base of circuits from a cycle matroid. The analysis uses the relationships between the number of mobile links, number of joints, and number of circuits in the base of circuits, together with the Latin matrix (whose entries are function of the absolute values of the partial gear ratios of the transmission). Calculating the rank of the Latin matrix can identify singularities, like groups of gears that rotate as a whole. Relationships between the output and input angular velocities and accelerations are then determined in a matrix-based approach without using any derivative operations. The proposed method has general applicability and can be employed for systems with any number of gears and degrees of freedom, as illustrated by the numerical examples presented.

No abstract

No abstract

No abstract

Based on recent results concerning the occurrence of function cognates in Watt II linkages, it is shown that only 3 geometric parameters are sufficient for defining the kinematic function of simplified planar rack-and-pinion steering linkages. The steering performances of the mechanisms are analytically expressed in terms of these parameters and, by employing an optimization-based synthesis method involving increasing the degree of freedom of the mechanism, the optimum domains are determined. The parameter sets corresponding to these minimum steering error domains are displayed in design charts. These charts aid the automotive engineer in the early stages of conceiving a new steering linkage by providing initial estimates of the basic geometry of the mechanism. They also provide information on two other characteristics of concern, i.e. the minimum pressure angle occurring in the joints and the rack stroke required for maximum turn of the wheels. [S1050-0472(00)00402-5]

The paper presents a novel technique for the kinematic analysis of bevel gear trains using the incidence matrices of an edge-oriented graph of the mechanism. The kinematic equations are then obtained in matrix form using a cycle basis from a cycle matroid. These equations can be systematically generated, and allow for an efficient computation of the angular velocities of the gears and planet carriers of the mechanism without employing time derivative operations. As illustrated in the paper, the method is applicable to bevel gear trains of any number of gears or degrees of freedom.