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Strategy for the Analysis of Relative Velocity and Relative Acceleration in Planar Motion

In a Nut Shell: Consider a simple example of the planar motion of three rigid links pinned together at

B and C as shown below. Start by examining the relative velocity of two points in link 1 where its planar motion is specified using the relative velocity equation shown below. Then proceed from this link to the next one (i.e. link 2), again using the relative velocity equation between two points on that link, such as B and C. Repeat this process until you have determined the linear and angular velocities for all links of interest. This procedure completes the analysis for relative velocity. Note that each relative velocity equation has two scalar components, one in the "i" direction and one in the "j" direction.

Next proceed to analyze relative acceleration. Use the "relative acceleration equation" for two points on link 1 where the planar motion is specified. As before proceed from this link to the next one, and so on, until all accelerations of interest (linear and angular) have been determined. Note the relative acceleration equation involves angular velocities. The values of these terms come from the relative velocity equation completed in the first part of the analysis. Also Note that each relative acceleration equation has two scalar components, one in the "i" direction and one in the "j" direction.

v_B = v_A + ω x r_AB

Relative Velocity Equation for Link 1

a_B = a_A + α x r_AB ˗ ω² r_AB

Relative Acceleration Equation for Link 1

Return to discussion of relative velocity. Return to discussion of relative acceleration.

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