Visualization of Relative Velocity and Relative Acceleration in Plane Motion

In a Nut Shell: The relative velocity and relative acceleration equations shown

below lend themselves to representation using vector diagrams. The vector on the

left hand side of the equal sign must equal the sum of the vectors on the right hand side.

Plots of these vector diagrams aid in understanding the physical nature of each term.

Summary:

v_C = v_A + v_C/A = v_A + ω x r_AC

Relative Velocity Equation

a_C = a_A + a_{C/A | n} + a_{C/A |t}

a_C = a_A + ω x ω x r_AC + α x r_AC

a_C = a_A ˗ ω² r_AC + α x r_AC

Relative Acceleration Equation

Meaning of terms Note: Both points, A and C, are in the same rigid link.

v_C is velocity of point C with respect to the fixed frame F

v_A is velocity of point A with respect to the fixed frame F

v_C/A is the velocity of point C with respect to point A in the fixed frame F

ω is the angular velocity of link B in the fixed frame F

r_AC is the position vector from A to C

a_C is the acceleration of point C with respect to the fixed frame F

a_A is the acceleration of point A with respect to the fixed frame F

a_{C/A | n} is the normal component of the acceleration of point A with respect to point C

in the fixed frame F

a_{C/A | t} is the tangential component of the acceleration of point A with respect to point C

in the fixed frame F

α is the angular acceleration of link B in the fixed frame F

α x r_AC is the tangential acceleration of C relative to A in frame F

- ω² r_ac is the normal acceleration of C relative to A in the fixed frame F

ω is the angular speed of link B in the fixed frame F

Click here to illustrate vector diagrams for relative velocity and relative acceleration.

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Copyright © 2019 Richard C. Coddington
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