Relative Acceleration for Links with 2 points in the same Link

Example: The figure below shows a model of the shoulder socket at A (fixed point), upper

arm, AB, lower arm BC, and a spinning disk of radius r with center at C. Point P of the

disk is directly to the right of C. The elbow at B is bent at 90^o. The following data:

AB = 0.45 m, BC = 0.675 m, r = 0.1 m, ω₁ = 5 k rad/sec, α₁ = 0 k rad/sec² ,

ω₂ = 3 k rad/sec, α₂ = ˗ 2 k rad/sec² , ω₃ = ˗ 5 k rad/sec , α₃ = ˗ 1 k rad/sec²

Find the acceleration of P at this instant. Find the acceleration of P relative to B.

Recall for any two points, R and S, in the same rigid link the relative velocity and

relative acceleration equations are:

v_R = v_S + ω x r_SR

a_R = a_S + α x r_SR ˗ ω² r_SR

Strategy: Apply the relative velocity and relative acceleration equation for each link, moving from the upper arm, to the lower arm, and finally to the disk. Typically you start with the

relative velocity equations first followed by the relative acceleration equations.

The relative velocity equation for the upper arm v_B = v_A + ω₁ k x (– AB i ) = - 2.25 j m/s

The relative velocity equation for the lower arm v_C = v_B + ω₂ k x (– BC j )

so v_C = 2.025 i - 2.25 j m/s

For the disk v_P = v_C ˗ ω₃ k x ( r i ) so v_P = 2.025 i - 2.75 j m/s (result)

Next apply the relative acceleration equations starting with the upper arm, AB.

Click here to continue with this example.

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