Question

Shown in figure is a Scotch yoke mechanism. What is the input and output motion of the mechanism? Derive (a) an expression for the position vector, Re, velocity, Vo=RB and acceleration, AB =Rp of the point B on yoke and (b) an expression for the position vector, RA, velocity, VARA and acceleration, AA =RA of the point A on slider in terms of 02, 02, d2 and O2A=a (crank length) y A 42 OzA=a 002 Ix B Position, velocity and acceleration of a vector in plane R = a cos(0) i +a sin(0) j, a: length of vector R VER -- a sin(O) i + a o cos(O)j A=V=R-a a [-sin(0) it cos(0) j|-a 02 (cos() i+sin(0)j]

Answer 1

Input crank will be rotational motion while output yoke will be a reciprocating motion.

Take $O_2$ as origin

a)

From the figure we can write position vector of B as

$\\R_B=O_2B i=O_2A\cos\theta_2 i=a\cos\theta_2 i \\ Velocity \\V_B=\dot{R_B}=-a\omega_2 \sin\theta_2i \\Acceleration \\ a_B=\ddot{R_B}=(-a\omega_2^2\cos\theta_2-a\alpha_2\sin\theta_2) i$b)

Position vector of A

$\\ R_A=a(\cos\theta_2i +\sin\theta_2j) \\ velocity\ of \ A \\ V_A=\dot{R_A}=a\omega_2(-\sin\theta_2i +\cos\theta_2j) \\ Acceleration \\ a_A=\ddot{R_A}=-a(\omega_2^2 \cos\theta_2+\alpha_2\sin\theta_2) i + a(\alpha_2\cos\theta_2-\omega_2^2\sin\theta_2) j$