We have studied effect of the flexibility of the connecting rod, the crank length and the slider mass on the dynamic behaviour of the mechanism。

3。1。Crank length

Small crank angles respect to the connecting rod lengths leads to a smaller amplitude of vibration and a more periodic  result。

3。2。Slider mass

As the mass of slider decreases amplitude of vibration of the connecting rod increases and a non-predictable answer obtains for both crank angle of the mechanism and amplitude of    vibration。

3。3。Flexibility of the connecting rod

EI 。π。4 Z   l πx

EI:l 。π。4

Increasing EI, leads to a more rigid mechanism, and the

U ¼ q12           

sin 2        dx ¼ q12       

2 l 0 l 4 l r

þmcg 2  sin  θ ð11Þ

where EI is the flexural rigidity。 The nþ1 equations of motion of the slider–crank mechanism can be written in the following format。 Now using the potential and kinetic energies defined and introducing the Lagrangian and taking the derivatives the equation of motion of the slider–crank mechanism obtains   in

this form

Mξ€ þBðξ; ξ_Þþ GðξÞþ F ¼ τ ð12Þ

where M is the mass matrix, which is symmetric and B involves the coriolius and centrifugal terms and G contains the terms of the gravity and the potential energy and F denotes the friction applied to the mechanism and τ is the applied torque at the crank。 The equation of the motion is then solved numerically using the ODE function of MATLAB software。 Thus the equations are first rewritten in the state-space  model。

3。Dynamic behaviour

In this section, effect of the mechanism’s parameters on the dynamic response of the system is investigated。 A single mode is considered for the connecting rod。 Since the connecting rod can be modelled as a pin–pin rod, a single mode is sufficient and accurate enough。 The mechanisms’ parameters used in the dynamic analysis are listed in Table  1。

amplitude  of  vibration  decreases  as  expected。  Phase  plane

diagram of θ shows a more periodic  response。

3。4。Constant angular velocity for crank

Considering a constant angular velocity for the crank eliminates one of the second order differential dynamic equations as the crank angle is known at each time。 In this situation amplitude of vibration of the connecting rod is the point of   interest。

The frequency response of the amplitude of vibration dependent on the mechanism’s parameters at constant crank angular velocity is studied。 Amplitude of vibration of connecting rod is plotted respect to the nondimensional crank angular velocity (Figs。   2–4)。动态行为障碍 - 曲柄机制相关联，具有灵活的连接性。参数包括曲线长度，接器和柔性元件的灵活性。方案是在弹性连接方式下进行的动力学振动抑制第一种方案是以反馈线性化为基础的，基于改进控制器。输入信号通过电压配置电机接地点，压电膜粘合到顶部和底部连接器的表面。控制器成功地反映了弹性连接的振动。