OCTOBER 19-20, 2012 - YMCA University of Science & Technology

Proceedings of the National Conference on
Trends and Advances in Mechanical Engineering,
YMCA University of Science & Technology, Faridabad, Haryana, Oct 19-20, 2012
Fig.2. Design curve obtained by optimization without considering clearance.
Table 1.Optimized value of variables
Design variables Optimized value
Without considering
clearance
L1(cm) 11.151457
L2(cm) 5.7811281
L3(cm) 14.227586
L4(cm) 14.227529
AP 28.455171
β (degree) 0.030539
e m Error
0.00712
Normalized(cm)
3. Analysis of design curve: considering joint clearance
In actual practice some clearances are in evitable in joints due to tolerances and defects due to manufacturing
process adopted or wearing after a certain working period. In this study it is assumed that links are connected to
each other by revolute joints with clearance. In the joint clearance, shown in Fig.3. r 2
is defined as the difference
between the radii of the pin and hole, r and r respectively. When the journal gives impact on the bearing
B
J
wall, normal and tangential force occurs. Also, if the friction is negligible, the direction of joint clearance vector
coincides with the direction of normal force at the contact point. When the continuous contact mode between
journal and bearing at joint is considered, the clearance may be modeled as vector which is similar to mass less
virtual link with length equal to joint clearance.
The equivalent clearance (clearance vector) can be defined in the form,
r2 = r B
− r J
(6)
Similarly r 3 can be defined.
Fig. 3. Equivalent clearance link
3.1. Synthesis Of Four Bar Path Generator With Joint Clearance
A four bar mechanism, as shown in Fig.4. is considered as an example to determine the effect of joint clearances
between crank and coupler link and between coupler link and follower link on path generation. Here we ve also
taken the coordinates ( X Y ) ( 0,0)
and the input angle θ 0 , in a local coordinate system.
0 , 0 =
1 =
249