An Analytical Study of the Dynamics of an Elastic Linkage

Abstract

The transverse vibrational characteristics of the connecting rod in a slider-crank mechanism are investigated. The equations of motion are derived, simplified, and solved. For the solution, two different numerical techniques are employed and correlation is achieved. Two dimensionless parameters, S the speed parameter and Z the physical parameter, arise during the derivation of the equations of motion. These parameters can be used by the designer as an indication of the vibrational activity of the mechanism.

Dynamic Interactions of Link Elasticity and Clearance Connections in Planar Mechanical Systems

“…For some time analysts have considered the effects of both link elasticity [1][2][3][4][5][6][7][8] 1 and connection clearances [8][9][10][11][12] on the dynamic behavior of planar mechanisms. Researchers have found that elasticity in the links of mechanisms has a substantial effect on the dynamic behavior of the mechanisms, while the results of the clearance studies have shown that the introduction of clearances in mechanisms causes substantial increases in the connection forces, resulting in degradation of the performance and life of the system.…”

The dynamic stability and nonlinear resonance of a flexible connecting rod: Continuous parameter model

“…where e0/represents the j-th order term in the expansion of e 0 which is defined in equation (9). Applying the same procedure to the equations of motion (25)- (27), the following sequence of equations is obtained:…”

“…Order e- 9 2 /~ = (e%)x = 0, (50) and (51), it is seen that b I = b 2 = 0. Hence, u~(x, To, Ta, T2) must be zero.…”

“…sin a =--, cos a --(10) tan a 1 + u~ 1 + e 0 1 + e 0 where e 0 is defined in equation (9). The connecting rod is assumed to be made of a viscoelastic material which is described by models built from discrete elastic and viscous elements.…”

“…Neubauer et al [9] examined the transverse deflection of an elastic connecting rod of a slider-crank mechanism by neglecting the longitudinal deformation, the Coriolis, relative tangential, and relative normal components of acceleration. By using the method of averaging and assuming a small length ratio, Jasinski et al [10,11] investigated the dynamic stability of a flexible connecting rod in a slider-crank mechanism.…”