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ENGR5004 / Week 7
Dynamics L13 Worked example 3TutorialOld spec ENGR2162:118 min

ENGR216 Dynamics L13 worked example 3 (slides 19-22) official answers

Crank AB (0.7 m) is pinned to the ground at A and is vertical at the instant shown, with B above A. It rotates anticlockwise with ωAB=3\omega_{AB} = 3 rad/s and αAB=2\alpha_{AB} = 2 rad/s2^2 (anticlockwise). Link BC connects B to a slider block C that moves in a straight guide inclined on a 3-4-5 slope (rising to the right: 4 horizontal, 3 vertical). At this instant C is 0.5 m to the left of A and 0.5 m below A.

Find the velocity and acceleration of the slider block C (and the angular velocity and angular acceleration of BC).

Vertical crank AB (0.7 m) about ground pin A, omega = 3 rad/s and alpha = 2 rad/s^2 anticlockwise; link BC down to slider C, 0.5 m left of and 0.5 m below A, in a guide on a 3-4-5 slope.
Vertical crank AB (0.7 m) about ground pin A, omega = 3 rad/s and alpha = 2 rad/s^2 anticlockwise; link BC down to slider C, 0.5 m left of and 0.5 m below A, in a guide on a 3-4-5 slope.
Formulas you may need
  • Fixed-axis rotation: v=ωrv = \omega r, at=αra_t = \alpha r, an=ω2ra_n = \omega^2 r (learn this)
  • vC=vB+ωBC×rC/B\mathbf v_C = \mathbf v_B + \boldsymbol\omega_{BC} \times \mathbf r_{C/B}, aC=aB+αBC×rC/B−ωBC2rC/B\mathbf a_C = \mathbf a_B + \boldsymbol\alpha_{BC} \times \mathbf r_{C/B} - \omega_{BC}^2\mathbf r_{C/B} (learn this)