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Kinematics of Relative Acceleration – Two points in the Same Rigid Link (Body)

(continuing discussion)

and finally a_C = a_A + dω/dt x r_AC ˗ ω² r_AC

which is the relative acceleration equation for two points, A and C, in the same rigid body

Summary:

v_C = v_A + ω x r_AC

Relative Velocity Equation

a_C = a_A + dω/dt x r_AC ˗ ω² r_AC

a_C = a_A + α x r_AC ˗ ω² r_AC

Relative Acceleration Equation

Meaning of terms

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

ω is the angular velocity of link B in frame F

r_AC is the position vector from A to C

dv_C /dt = a_C is the acceleration of point C with respect to the fixed frame F

dv_A/dt = a_A is the acceleration of point A with respect to the fixed frame F

dω/dt x r_AC is the tangential acceleration of C relative to A in frame F

dω/dt = α is the angular acceleration of link B in frame

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

ω is the angular speed of link B in frame F