Calculate Force to Lift Weight in Multi-Scissor Lifts

[Timma300]

Hello, I am building a scissor lift for a design project. I located a formula for calculating the amount of force required to lift a weight as given:

F=(W+(Wa/2))/(tan(theta))

Where F is the amount of force required, W is the weight of the payload and the load platform, Wa is the weight of the scissor arms, and theta is the angle that the scissor makes with the horizontal. I found the equation here, on this webpage: http://www.engineersedge.com/mechanics_machines/scissor-lift.htm. I understand that the higher the scissor lift is raised, the less force that is required to raise it. My question is about a multi-scissor lift. The site describes the equation for a multi-scissor lift as the exact same equation, except you multiply F by the number of stacked scissor mechanisms. Does this mean that a double scissor lift will require half as much force or twice as much force to raise?

 

[Timma300]

For those of you that are wondering like I was, I ran an experiment to figure this out. I created a small 2-tier scissor lift that resembled a small double set of hedge trimmers. I braced the bottom of the scissors against a board clamped to the table and the other against a board of a decent amount of weight. I pushed the two scissors together and made a note of the force required, and then removed the second tier and repeated the experiment with one scissor. With the one tier scissor, I repeated the experiment and it took half as much force as the first test, it was much easier to push. The result of the second test proved that for each level you add to the scissor, you are multiplying the amount of force it takes to lift. This means that if you make a double scissor lift, it would take twice as much, a triple lift would take three times as much and so on. Hope this helps anyone else out there who was also confused.

 

[R4de0n]

Thanks Timma, helped me in my calculations. Was contemplating using two tiered scissors but decided against it.