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ENGR5004 / Week 8
ENGR216 2023 Dynamics Q B2Past paperOld spec ENGR216First25 marks30 min

ENGR216 Summer 2023 Dynamics Q B2[VALID]

Figure B2 shows a crank driven assembly that comprises three connected slender bars (AB, BC and CDE) that produce oscillatory motion at point E. Each of the bars are of uniform section and have a mass moment of inertia for zz-zz rotation about their centre of mass (IGI_G) of 112ml2\frac{1}{12}ml^2, where mm = mass and ll = length. Data: AB = 0.3 m, BC = 0.5 m, CD = 0.3 m, DE = 0.6 m, θ˙=10\dot{\theta} = 10 rad/s. For the instant shown:

Figure B2: crank AB (vertical, pinned at A) driving link BC and bar CDE pivoted at D; CDE horizontal.
Figure B2: crank AB (vertical, pinned at A) driving link BC and bar CDE pivoted at D; CDE horizontal.
Formulas you may need
  • Rigid-body relative velocity: vB=vA+ω×rB/A\mathbf{v}_B = \mathbf{v}_A + \boldsymbol\omega\times\mathbf{r}_{B/A} (learn this)
  • Rigid-body relative acceleration: aB=aA+α×rB/A−ω2rB/A\mathbf{a}_B = \mathbf{a}_A + \boldsymbol\alpha\times\mathbf{r}_{B/A} - \omega^2\mathbf{r}_{B/A} (learn this)
  • Instantaneous centre of zero velocity (as a check) (learn this)
  • Slender bar: IG=112ml2I_G = \tfrac{1}{12}ml^2 (given in the question)
  • Parallel-axis theorem: ID=IG+md2I_D = I_G + m d^2 (learn this)
  • Planar kinetics: ∑F=maG\sum\mathbf{F} = m\mathbf{a}_G, ∑MG=IGα\sum M_G = I_G\alpha; about a fixed pin ∑MD=IDα\sum M_D = I_D\alpha (learn this)
  1. (i)
    Show that the velocity of point B is −3i-3\mathbf{i} m/s
    [2]Third
  2. (ii)
    Show that the velocity of point C is 4j4\mathbf{j} m/s
    [3]2:2
  3. (iii)
    Determine the angular velocity of bar CDE
    [3]Third
  4. (iv)
    Determine the angular accelerations of bars BC and CDE
    [6]2:1
  5. (v)
    Determine the acceleration of the centre of mass of BC
    [5]2:2
  6. (vi)
    Given that the mass of BC = 2 kg and the mass of CDE is 3 kg, determine the forces exerted on BC by the pins at B and C.
    [6]