Scotch yoke actuator equation

[tstittle]

thread404-300325

It was noted in this previous thread that a scotch-yoke actuator has a strange relationship between angle of rotation and output torque. The torque vs. angle curve is a parabola shape. None of the many answers actually gave a useful solution to the question. I recently figured this out and found this thread and thought I would post a more helpful solution. See attached force balance.

The reason this is counter-intuitive is because the output force normal to the lever arm of the actuator is actually greater than linear output in the cylinder (Pressure * Area). It works this way because of the direction of each reaction force as shown.

 

[EngineerErrant]

Thanks for puzzling this one out. It's been bugging me.

"Engineers like to solve problems. If there are no problems handily available, they will create their own problems." -Scott Adams

 

[zekeman]

A first course in physics shows that the torque is equal to the normal distance to the external force
vector times the amplitude of that force, FXR.=FRsin(theta) and Rsin
(theta) is constant.

So, given that the force vector is constant, it must follow that the torque remains constant for this problem, period.

So exactly where is the mystery?

The higher force on the slot is accompanied by the lower normal distance so that, the torque is the same.

 

[rb1957]

with zeke on this ... surely a simple problem to solve.

 

[btrueblood]

The OP has the normal force going infinite when angle = 90 degrees. Sounds problematic to me...anybody got some of that unobtainium for the slot and pin?

 

[rb1957]

yes, 'cause when the link is vertical there is nothing in the assumed reactions to react horizontal load.

which makes me question the load balance on the link ... if this is a two force member, then the two forces need to have the same link of action, which would imply they acting along the slot (not across it as assumed). which would imply that the only time the original assumption "static equilibrium" is achieved is when the valve is fully open or fully closed, when both pins are bearing against the ends of the slot.