This type of Grashof linkage is obtained when the shortest link is the floating link (r3). Note that the complete relative motion between the shortest link and its adjacent links are still possible. Both the input and output links have limited ranges of motion that are defined as follows:
lower limit: theta2 = theta1 + theta2'
upper limit: theta2 = theta1 + theta2''
where theta2' = acos [ ( r1^2 + r2^2 - ( r3 - r4 )^2 ) / ( 2 * r1 * r2 ) ]
theta2'' = acos [ ( r1^2 + r2^2 - ( r3 + r4 )^2 ) / ( 2 * r1 * r2 ) ]
lower limit: theta4 = 180 + theta1 - theta4''
upper limit: theta4 = 180 +theta1 - theta4'
where theta4' = acos [ ( r1^2 + r4^2 - ( r3 - r2 ) ^2 ) / ( 2 * r1 * r4 ) ]
theta4'' = acos [ ( r1^2 + r4^2 - (r3 + r2)^2 ) / (2*r1*r4) ]
To see animations of this linkage select the links below: