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ENGR5004 / Week 8
ENGR216 2017 Q B2Past paperOld spec ENGR2162:125 marks30 min

ENGR216 Summer 2017 Q B2[VALID] official answers

Answer ALL parts (a) - (d).

In a food factory, a machine for processing confectionery consists of two rollers mounted on a carriage which moves back and forth over a base plate. Confectionery mixture is placed on the base plate and movement of the carriage rolls the confectionery material out until the desired thickness is achieved. A crank OA and connecting rod AC are used to move the carriage back and forth (Figure B2). The crank is driven by a geared electric motor.

The following particulars are given:

  • Crank radius a: 1.2 m1.2\ \mathrm{m}
  • Connecting rod length b: 4.5 m4.5\ \mathrm{m}
  • Crank rotation speed (constant): 30 rev/min30\ \mathrm{rev/min}
  • Mass of carriage, including rollers, m: 55 kg55\ \mathrm{kg}
Figure B2: crank OA (length a) pivoted at the fixed point O, at angle theta above the horizontal, turning counter-clockwise (curved 'Direction of cranking' arrow); connecting rod AC (length b) runs down to the right to pin C on the wheeled carriage, at angle beta from the vertical through C; the carriage rolls horizontally on a flat base plate.
Figure B2: crank OA (length a) pivoted at the fixed point O, at angle theta above the horizontal, turning counter-clockwise (curved 'Direction of cranking' arrow); connecting rod AC (length b) runs down to the right to pin C on the wheeled carriage, at angle beta from the vertical through C; the carriage rolls horizontally on a flat base plate.
Formulas you may need
  • Angular speed conversion ω=2πN/60\omega = 2\pi N/60 (rev/min to rad/s) (learn this)
  • Relative velocity vB=vA+ω×rB/A\mathbf{v}_B = \mathbf{v}_A + \boldsymbol\omega \times \mathbf{r}_{B/A} (given in the 2017 Section B formula sheet; not on the 2026 sheet, so learn this)
  • 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} (given in the 2017 Section B formula sheet; learn this)
  • Instantaneous centre ω=vA/rA/IC=vC/rC/IC\omega = v_A/r_{A/IC} = v_C/r_{C/IC} (given in the 2017 Section B formula sheet; learn this)
  • Fixed-axis rotation at constant speed: aA=−ω2rA/O\mathbf{a}_A = -\omega^2 \mathbf{r}_{A/O} (learn this)
  • ∑F=maG\sum \mathbf{F} = m\mathbf{a}_G for the translating carriage; a light pinned rod is a two-force member (given in the 2017 Section B formula sheet / learn this)
  1. (a)
    When the crankshaft is in the position shown, angle θ\theta is 30∘30^\circ and angle β\beta is 60∘60^\circ instantaneously. Find the velocity of the carriage when in this position and the angular velocity of link AC.
    [10]2:2
  2. (b)
    Find the acceleration of the carriage for the same position.
    [7]
  3. (c)
    Find the angular acceleration of link AC for the same position.
    [3]2:2
  4. (d)
    When there is no confectionery mixture on the base plate, the carriage rolls with very little friction. For this case, find the force in the connecting rod for the position shown in Figure B2.
    [5]