Bar-slider-bar Linkage Analysis

Linkage

Link 1 is a frame

The slider is on link 2

Link 3 is a driver

Vector equation:

r₁ + r₃ = r₂

1. Position

Given: L₁, L₃ lengths of the frame and driver

θ₁, θ₃ angles of the frame and driver

Solving: r_2, θ₂ position of the slider, angle of bar 2

Components equations in x and y directions

x:

y:

+

Solution:

If θ₁ = 0, horizontal frame

If θ₁ = 90°, vertical frame

2. Velocity

Given: L₁, L₃, r₂ lengths of the links, and position of the slider

θ₁, θ_2, θ₃ angles of the links

ω₃ angular velocity of the driver, bar 3

Solving: v₂, ω₂ velocity of the slider, and angular velocity of bar 2

Consider as a horizontal frame, θ₁ = 0,

Take derivatives of the position equations

x:

y:

Rearrange

Solution:

3. Acceleration

Given: L₁, L₃, r₂ lengths of the links, and position of the slider

θ₁, θ_2, θ₃ angles of the links

v₂, ω_2, ω₃ velocity of the slider, and angular velocity of links

α₃ angular acceleration of the driver

Solving: a₂, α₂ acceleration of the slider, and angular acceleration of bar 2

Take derivatives of the velocity equations

x:

y:

Rearrange

Solutions: