Below is a copy of a blog post I made today:
Assume that we have a scissor lift that we use to lift W lb of sacks to a height of 36 inches.
Also assume that the lift is actuated by a center pin torque with gearing ratio GR that is the output torque/motor torque.
A N stage scissor lift requires a center torque = N*(W_lb + W_lift/2)Lcos(phi) where phi is the interior angle between the arm and the base (see this scissor theory post).
The max torque occurs when phi = 0 or when the lift is at its lowest point. At this point the total torque = M* m_torq where M is the number of motors and m_torq = max motor torque set by the PTC limits.
m_torqM = N(W+W_lift/2)*L/GR or
W = GRm_torqM/L/N – W_lift/2
Lets put in some typical numbers: L = 6 in, W_lift = 1 lb, N = 4 , GR = 7:1, m_torq = 6 in lbs (the 6 in lbs is set by alloting 3.5 amps per two 393′s driven by half a cortex or power expander.)
W = 1.75*M – .5 lbs
M motors => lbs (sacks)
1 => 1.25 lbs (2.5 sacks)
2 => 3 lbs ( 6 sacks)
3 => 4.75 (9.5 sacks)
4 => 6.5 lbs ( 13 sacks)
Focusing on the 4 motor case, lets see what happens when elastic is added that pulls with an upward force on the center pivot. In this case, when the robot is picking up sacks, the motors would be holding the lift down against the elastic. When the lift goes up the elastic and motor are working together. If we add just enough elastic that the motor can still hold the lift down then this is equivalent to doubling the motor torque when the lift is down. So
Elastic +4 => 13.5lbs (27 sacks)
Or we could also up the gearing ratio by x3 factor…. the lift would be 3 times slower but here you would be making one large dump and speed is not required.
3x gear + 4 => 20.5 lbs(41 sacks)
Ok now we are talking…. 41 sacks !! But in Mythbusters style…. more is better so how about 6 motors.
3x gear + 6 => 31 lbs (62 sacks)
Ok… enough for me. Not sure how you would stack 62 sacks on the upper goal. These numbers are of course rough cuts and ignore friction etc but elastic can be use to make the theory come true.
So in summary, looks like we should be able to lift 13 sacks to a 36 in height with 4 393′s working through a 7:1 gearing ratio. Adding elastic can increase this to 27 sacks or using a 21:1 gearing we can get to 41 sacks or with a 21:1 gearing and 6 motors we can lift 61 sacks.