This document describes an offset crank-slider mechanism and provides instructions to write vector loop equations for it, differentiate the equations to obtain velocity equations, and identify the two unknown velocities in the equations. Specifically: - It describes writing vector loop equations separating the X and Y components for the mechanism, with dimensions provided in mm. - Differentiating the vector loop equations results in two velocity equations, with the unknown velocities being ω3, the angular velocity of link 3, and V4, the velocity of link 4 in the y direction.

1. The mechanism above is an offset crank-slider mechanism. Dimensions are in mm. Write a
vector loop equation for this mechanism, with the X and Y components separated. Differentiate
the vector loop equation to obtain the two velocity equations. Which are the two unknown
velocities in the velocity equations?
Solution
a) let theta2 and theta3 be the angles of the links 2 & 3 from positive x axis
L2cos(theta2) + L3cos(theta3) = offset
63cos(theta2) + 130cos(theta3) = 52 ( X component vector loop equation )
L2sin(theta2) + L3sin(theta3) = Y4
63sin(theta2) + 130sin(theta3) = Y4 ( Y component vector loop equation )
b) -63sin(theta2)*omega2 - 130sin(theta3)*omega3 = 0 (first velcocity equation obtained
by differentiating x commponet of vector loop equation)
63cos(theta2) + 130cos(theta3) = V4 (second velcocity equation obtained by
differentiating y commponet of vector loop equation, V4 is the velocity of link 4 in y direction)
c) The two unknowns in this mechanism are omega3 and V4 .