When r1 + r2 < r3 + r4 the input link (r2) of the linkage is said to be inward limited.
When r1 + r4 < r2 + r3 the output link (r4) of the linkage is said to be inward limited.
When a link is inward limited there are limits on the possible values of the angle of the link that the actual angle must remain outside (the link is limited when moving in the inward direction).
The limits are defined as follows.
Input Link
lower limit: theta2 = theta1 + theta2'
upper limit: theta2 = theta1 + 360 - theta2'
where theta2' = acos [ ( r1^2 + r2^2 - ( r4 - r3 )^2 ) / ( 2 * r1 * r2 ) ]
Output Link
lower limit: theta4 = theta1 - 180 + theta4'
upper limit: theta4 = theta1 + 180 - theta4'
where theta4' = acos [ ( r1^2 + r4^2 - ( r2 - r3 )^2 ) / ( 2 * r1 * r4 ) ]
To see animations of this linkage select the links below:
