ENGR273 2026 Q3 (ENGR5004)

ENGR273 2026 Q3Past paperCurrent spec2:125 marks30 min

ENGR273 Summer 2026 Q3[VALID] official answers

The planar mechanism in Figure Q3-1 comprises a crank OA (uniform slender rod of length $a$ , mass $m_1$ ) pinned at O, and a coupler AB (uniform slender rod of length $b$ , mass $m_2$ ) pinned at A and at the slider point B. Point B is a frictionless slider of mass $m_3$ constrained to move along the vertical guide at $x = d$ . At the instant shown, OA is horizontal along $+x$ , so $A = (a, 0)$ . The slider is at $B = (d, y_B)$ with $y_B > 0$ . The slider velocity and acceleration are known and upward:

$\mathbf{v}_B = v_B\,\mathbf{j}, \qquad \mathbf{a}_B = a_B\,\mathbf{j}.$

Neglect gravity and all frictions of the whole system. Positive angular sense is counterclockwise $+\mathbf{k}$ .

Figure Q3-1: crank-coupler driving a vertical slider at x = d.

Formulas you may need

Rotation about a fixed axis: $\mathbf{v} = \boldsymbol\omega\times\mathbf{r}$ , $\mathbf{a} = \boldsymbol\alpha\times\mathbf{r} - \omega^2\mathbf{r}$ (learn this)
Relative velocity $\mathbf{v}_B = \mathbf{v}_A + \boldsymbol\omega\times\mathbf{r}_{B/A}$ (learn this)
Relative acceleration $\mathbf{a}_B = \mathbf{a}_A + \boldsymbol\alpha\times\mathbf{r}_{B/A} - \omega^2\mathbf{r}_{B/A}$ (learn this)
Equations of motion $\sum\mathbf{F} = m\mathbf{a}_G$ , $\sum M_G = I_G\alpha$ (or $\sum M_O = I_O\alpha$ about a fixed pin) (learn this)
Slender rod $I_G = \dfrac{1}{12} m L^2$ , $I_O = \dfrac{1}{3} m L^2$ about an end (learn this)

(a)
Draw the free-body diagrams and kinetic diagrams for OA, AB, and the slider at B. Clearly state your axes and indicate all unknown reactions at pins/guide.
[8]2:2
(b)
Determine the instantaneous angular velocities $\boldsymbol{\omega}_{OA}$ and $\boldsymbol{\omega}_{AB}$ , expressed in terms of $a$ , $b$ , $d$ , and $\mathbf{v}_B$ .
omega_OA (CCW +) =v_B/a
omega_AB (CCW +) =rad/s
[8]2:2
(c)
Determine the instantaneous angular accelerations $\boldsymbol{\alpha}_{OA}$ and $\boldsymbol{\alpha}_{AB}$ , expressed in terms of $a$ , $b$ , $d$ , $\mathbf{v}_B$ , and $\mathbf{a}_B$ .
alpha_AB (CCW +) =v_B^2/(a*y_B), y_B = sqrt(b^2-(d-a)^2)
[9]