Use lever arms, and a linkage. Put one of the lever arm arms on the servo. Set up an axle with a lever arm on it also. Figure out the length of the lever arm on the axle such that 180 degrees of motion on the servo moves the lever arm on the axle 90 degrees. Those 90 degrees should be centered in such a way that when the servo arm is at 1/2 of it's turn, the axle will be at half of it's turn.
Now for BAD ascii art.
Code:
Linkage Linkage Linkage
l |
l |
l |
l |Servo Servo Servo|
l |Servo Servo Servo|
l |Servo Servo Servo|
Axle
Axle
In this diagram, since the servo arm is shorter than the output arm, it will move the "Linkage Linkage Linkage" near(I didn't do any calculations for my bad art) 90 degrees for 180 degrees of servo motion.
Also just thinking out loud, Could you possibly use two servos. You could place the servos on opposite sides of the mechanism, and after writing some code to reverse the pwm values, you would have two servos, and therefore double the torque, working on actuating one mechanism.
Good luck. If this does not make sense, ask again, and I bet someone can draw a better* diagram.
*Not ascii art