## 4 Bar Balance Notes

While discussing 599D team approach to balancing their 4 bar I decided to do a little calculation to see whether a Vex black surgical tubing would suffice and how much is required.  The 4 bar is 17 in long and 2 inches in width.

Vex motor friction torque:   I made a rough measurement of the kinetic friction of the 393 motors.   One motor could hold 1 inlb of torque or about  8 % of the max torque.    A legacy 3 wire motor has slightly less at 13 oz in.

393 friction torque applied to a typical 4 bar robot:

The 599D  four bar lift  requires 3 3/8 lb to hold the lift level at 11 inches from the pivot or 37 in lbs of torque.    Four tubes weight about 1 lb so lifting 4 tubes adds 17  in lbs.  The beauty of a four bar  is that even though the tubes cg is at about 20 inches, the weight can be considered to be centered on the edge of the 4 bar.

So to hold a 4 bar that is loaded would require about 54 inlbs of torque.    The D robot currently uses two 393 motors with linear slides doing the lifting.    This is ok, but the lifts are not synchronized.

One possible solution is to move the motors and do a standard pivot drive.       The minimum gear ratio to handle 54 inlbs  with motors running at peak power (about 6.5 inlb/50 rpm) would be 54/13 = 4.15 or rounding a 5 :1 gearing would be adequate.   The lift time (60 deg arc) = 60/360/50 rpm*60sec/min *5= 1 sec.       Above, I calculated that the holding friction is only 1 lb per motor so with the 5:1 gearing,  friction only supports 10inlbs so the lift will be unbalanced by about 44 in lb.   The would need to be  supported by the motors outputting a holding torque of about  44/(26*5)*127 = 43 pwm counts (34% max torque) which calls for about 1.4 amps per motor.  This is doable for an extended period of time but there would be heating of the motor fuse and this in turn would limit the motor max torque.   What about using elastic counter force to help the balance.

Adding an elastic tubing counterbalance to a 4 bar:

Way back in Dec I measured the elastic constant of a 10 ft vex rubber tube folder twice to get a 4 strand 2.5 ft segment.  The 4 strands delivered about .2 lbs /per in.  up to max of 4 lbs  at roughly twice the original length.     Therefore a single strand gives .05 lbs per in.

So if we mount the tubes vertically pulling down on a  4 in lever sticking out of back of the 4 bar we can assume a total length of 15 inches when stretched then we can  use two  10 ft cords (one Vex pack) each folded over 4 times to get  32  7.5 in segments that give .375 lbs when stretched to 15 inches.(total of 12 lbs per 32 segments) .   This then gives 48 in lbs on a 4 in lever and meets the balance torque needs.     If the 4 bar is neutrally balanced , then we can use something closer to the max speed (100 rpm) to determine lift time so it would lower the time to .5 sec.

Using Elastic like a desk lamp 4 bar

A 4 bar desk lamp has a spring tension from the top pivot to the bottom bar to provide a counter balance to the lamps weight.  We can do a similar thing with the 599D 4 bar.  If we assume the same 32 7.5 in segments (16 on each side)  we will get a diagonal force of  12 lbs.  The balance torque provided is vertical component of the force  times the length which is

is roughly the width/(diagonal length) * diagonal force*length  = 2/18*12*17 ~=24 in lbs.  So with two 10 ft cords we can cut the unbalanced torque to 20 in lbs (=54-10-24).   This cuts the hold currents nearly in half and is very doable.    If you add another two cords, then the 4 bar is essentially balanced.

Doubling the gear ratio to minimize elastic force required

Using a 10:1 gearing doubles the lift rise time (unbalanced) to 2 sec.  The holding friction torque  is more than doubled to 20 inlb leaving 35 lbs of unbalanced torque.