For figure shown below determine the position velocities and

For figure shown below, determine the position, velocities, and acceleration for the offset sliding contact linkage. Assume r_0, r_1, e, Omega_1, theta_1, is given. Link 2 and offset e is perpendicular to each other. (Write detailed steps)

Solution

solution:

1) for 4 bar chain mechanism with sliding pair there is induction of corolis component in accelaration

2)hence solving for four bar chain we can solve for slider subject to rotation about joint of 2 and 3 link

3) here loop closure equation is

R1\'+R2\'+R3+Ro\'=0

where here r1,e,ro are known and angle a1,ao is known

from geometry of mechanisn as third link is offset to first link hence at given instant

cosa1=r1-e/ro

where

a3=a1

and angle a2=a3+90

as all angle and three vector magnitude are known hence magnitude of second vector r2 can be known by loop closureequation and its angular velocityw2 and a2 also known by differentiating loop closure equation

3)once r2 is known to calculate velocity and accelaration of slider point let consider vector arising from joint of link 2 and link 3 upto slider point that is vector R2\'

hence for slider position is given by

R2\'=R2(cosa2i+sina2j)

on differentiating we get velocity of link 2 ,it will also give velocity of slider as

r2w2=(-r2*sina2w2+Vscosa2)i+(r2cosa2w2+Vs*sina2)j

where vs=velocity of slider

on differentiating we get accelaration of slider as

for eqauting imaginary part we get

f=r2w2^2sina2-2*Vs*w2cosa2/sina2

5) in this way above mechanism can be analysed if we combine simple four bar chain mechanism and sliding block over vector toghether