# Gearing/motor questions.

Hi everybody, I’m here to ask for a little bit of shared knowledge regarding arm control. Team 448’s arm for this year (still conceptual) is all laid out except for our motors and gearboxes. We are working with the kitbot chassis, and using both gearboxes and 4 CIM motors for the drive wheels. We considered using the FP motor (tilt) and tageine motor (lift) to power our arm, but would like your opinions.

I have two separate questions –

1. The arm will telescope using a cascading cable system (lots of tension, but less length to move the cable). Our empty arm will weigh approximately 18lbs, or 27lbs with a vision tetra (not counting potential friction). Though the arm extends about 15 feet, we will only need to move about 6 feet of cable as our arm extends every segment at the same rate. This needs to be quick and most importantly reliable. How would you suggest powering a drum to wind the cable? We also need to know how to figure out the proper drum diameter for the extending segment and the contracting segment (they work at different speeds). Also, links to cable drums that are FIRST legal would be appreciated.
2. The arm must be able to tilt with a tetra on it while extended. This is another cable mechanism, powering the arm both forward and back. A 9lb tetra + an 18lb arm, over 15 feet should be able to travel to about 30 degrees forward of vertical and 5 degrees back. Due to constraints on our CG, this system must be low to the ground (maybe a foot above the base of the arm, tops). Speed is not so much of an issue, but it is always nice to have. Back drive does not need to be eliminated, but reduced, if possible.

Thank you!
Joshua Siegel

I cannot recommend a gearing based on the information provided.

I do want to caution you on using a cascading extension lift for too many extension sections. The forces on your bottom cable will get very high. As I recall it is an exponential increase with each extension section (2 to the x power - where x is the number of extensions above the fixed one). Do a free body diagram of each section to figure out the tension on each cable and you will see what I mean.

Raul

Would you reccomend using a continuous cable system instead? The switch wouldn’t be too hard, especially since we haven’t started building, but I’ve heard those like to bind at the most inopprotune times, and you can’t fix it on the fly like you can with cascading (reverse/forward again). Currently, we have 3 segments each weighing about 3lbs and some hardware to mount them, and a 4th piece on a slider with a pneumatic cylinder. 900lb cable (3/32" steel cable) should be fine for the load, but maybe the motors will be running too close to stall at that point. I did some math, but its probably off by (quite) a bit.

Fobject = 13lb
Dobject = 30"
Mslider = 13lb30" = 390lb"
Fslider1 = 390lb"/(2
12") = 16.25lb
Fhit = .5390lb" = 195lb"
Mhitlower = 195lb"50"+(390lb"(50"/2")) = 19500 something?
Flower1 = 390lb" + 19500/(2
20") = 877.5
Mhit = 195lb" * 130" + ((15lb*.5*130"))/2 = 812.5 something
Mbase = 390lb" + 812.5 something = 1202.5

Does that look reasonable for numbers? What about doability? I’m really liking the way cascading works, if its at all possible for us to do. A redesign at this point would set us back quite a bit, if continuous wouldn’t work either.

edit: More usable math for potential gearing.

Telescoping drum – 2.5” diameter drum:

1. Speed - 2.5” radius drum, pi2.5”^2 = 19.5” circumference, 19.5” per rotation. Must move 60” of cables in order to fully extend. 60”/19.5” = 3.1 turns. Desired time should be about 5 seconds to telescope, so output must be ~37.2 RPM. Can be as low as 25 rpm.
2. Force – Will be lifting approx. 27lbs straight up, and headroom is needed. Gear for 35lbs.
Lever arm is theoretically the radius of the drum (2.5”). Force is 35lbs, to include some friction or potential weight discrepancies when the pneumatic cylinder is pressurized. 2.5” = .208’ * 35lb = 7.2 ft-lb.
Torque of the taigene motor @ 60RPM (12V) is 5.7 newton meters. 5.7 * .737562 = 4.2 foot lbs. Gear the motor down 2 to 1, you have 30 RPM and 8.4ft-lbs of torque, while still telescoping fairly quickly. Could gear down to 2.5 to 1 for 24RPM and 10.5 ft-lbs, assuming no loss to friction. Telescoping would take about 9 seconds at this point, likely too slow for autonomous, but the motors will not heat up like the FP motors after repeated use.

Telescoping drum – 3” diameter drum:
3. Speed - 3” radius drum, pi3”^2 = 28.2” circumference. 60”/28.2” = 2.1 turns. 5 seconds to telescope, so output ~25.2 RPM ((2.1/5)*60). 16 rpm for 8 seconds to telescope.
4. Force –35lbs.
Lever arm is 3”. Force is 35lbs. 3” = .25’ * 35lb = 8.75 ft-lb.
Stock torque is 4.2 foot lbs @ 60 rpm. Gear the motor down 2.5 to 1, you have 24 RPM and 10.5ft-lbs of torque, while still telescoping in 5 seconds. Could gear down to 3 to 1 for 20RPM and 12.6 ft-lbs, assuming no loss to friction.

Does this make sense? This basically tells me that the gearing on the motor should be based on torque and the diameter of the drum should be based on speed. The 3” drum looks a little more powerful at speed, but doesn’t it also take more power to move? I’m really starting to get lost in the math :S

First I want to tell you that we have done a continuous cable lift many times and have never had a problem.

I am having a hard time following your math. But, before you go too far, check the feasibility of your concept:

[font=‘Times New Roman’]1) First do a simple calculation to determine if any motor can do what you wish to do.[/font]

[font=‘Times New Roman’]- Power = distance*force/time.[/font]

[font=‘Times New Roman’]- Example: need to lift 10 lbs, 10ft in 2 seconds -> Power required is 50 ft-lb/sec, which is about 0.1 HP or 75Watts. [/font]

[font=‘Times New Roman’]- If you choose a motor with more power than you need, you can gear it to run a little faster and be more efficient. If you choose a motor with less power, it simply will not be able to lift the load as quickly and will have to be geared accordingly.[/font]

[font=‘Times New Roman’]2) Pick the proper gearing for the drum diameter.[/font]

[font=‘Times New Roman’]- Since you know how much distance you get with one rotation, you can now choose the gearing that will allow the chosen motor to move it at the chosen speed. [/font]

[font=‘Times New Roman’]- Example: 5” OD drum you chose can move 10ft in a little more than 6 turns, so you need to go 3 RPS or 180 RPM in order to lift the 10 pounds, 10ft in 2 seconds.[/font]

[font=‘Times New Roman’]- Again, you cannot accomplish this if the motor does not have enough power. [/font]

[font=‘Times New Roman’]- Using the motor curve you choose you can compare it RPM at peak power to the RPMs you need and that tells you the gear ratio you need.[/font]

This was just a quick guide, I think there are white papers on CD that tell you how to pick a gear ratio.

Thank you, I’ll look into the continuous cable systems. From what I understand, they offer lower tension at the cost of having to move more length of cable, which means a faster motor with the same ability to exert a force.
I’d really like to use continuous, but I’m worried about the speed. Assuming the force needed (not tension) to move the object is the same, cascading is much faster which will become critical in autonomous mode. This would allow us to gear a motor down for more power and have it lift the tetra in the same amount of time.

edit:
Here’s what I’ve got on the new calculations for continuous, I just need to find out how to relate the power of the motor and the power needed to lift the arm.
Power = 12.6ft * 35lb/5 seconds
Power = 88.2ft-lb/sec = ~.18hp or 132.3 watts
Taigene motor specs (ungeared) – 5.7Nm @ 63RPM @ 12V. 5.7Nm * 0.738 = 4.2 ft lbs. 67 watts
3” diameter drum = 28.2” circumference. 152”/28.2 = 5.4 rotations.
5.4 rotations in 5 seconds, so 65RPM.

So is it…
88.2ft-lb/s/63 rotations = 1.4ft-lb/rotation = 33% of stall output, appropriate for direct drive?
or
4.2ft-lb/1.08RPS = 3.89ft-lb/s where the motor is underpowered?

I also ran the numbers through JVN’s gear calculator with a 1:1 ratio and 3" torque arm radius. Stall load is 81.42lbs. With an applied load of 30lb (tension of the cable), it says the motor load torque is 10.2Nm. Seems like this motor is underpowered…

Maybe cascading 3 to 1 is the way to go, if this design must be used. The CIMs are all taken up, the FP needs to be running to cool itself (so it can’t hold the arm) and the globe motor is too slow according to 61 who used it to telescope a continuous arm in 2004.

Josh

Hey guys - help out some newbies here. We are interested in a continuous extension lift but are having difficulty getting our heads around the details of the cabling - attachment points and all that. WE have a PP from JVN but nothing that gives us the ability to sort it out in hardware terms. Any help out there with pictures or doc that are explicit?

Thanks!

For the past several years the BeachBots have used a cascading lift. Last year our “sliding” gear box, which enabled us to slide sdieways on the bar, weighed as much as a tetra. So the lift we used last year should work for what you want easily. I don’t have the numbers handy here at work so I can’t tell you the calculations we used. But I can tell you about the winch.

We used two stock FP motors and gearboxes. We used the “jeep driver” plastic parts to connect to a drum of slightly larger diameter. The winch was somewhat over powered as we made it strong enough to lift a second robot should we get entangled. The winch had three cables on the same drum, two “upgoing” for extending the lift, and one “downgoing” for retracting it. All were on the same drum at the same diameter.

The first stage of the lift had a pulley system that “slowed down” and extended the up going cable. This allowed the cable to move the same speed whether it was going up or down. I’ve attached a sketch of how we did it.

Great, thank you!

Out arm extension mech last year used the same basic system as the one just above, continuous cable, FP motor (one with gear box) with it’s plastic hub as the cable drums, we used three total plastic hubs from the kit of parts as the cable drums, we also linked a window motor to the 1/2 inch shaft for the hold when not powered. The free speed ratio last year worked out to 1.4:1 this year the free speed at 12.2 volts on a FP and gear box is 144,(last year it was 130) free speed of the Nippon window motor is about 78 to 80 not the published 75 this is at full battery voltage. 12.2 to 12.4, You windup putting the larger sprocket on the window motor to match the shaft speed of the FP. (Removed clip, remove geared hub from window motor, weld thick washer to drive teeth, drill and tap 4 or so holes through washer bolt flat #35 sprocket to washer with #8 or #10 button top cap screws, watch out for chain clearances. Put back together.) I would not recommend running the FP at or near stall at 12 volts, we let the smoke out of two last year. Also the window motor takes load well as long as the hold direction pushes the driving worm away from the motor, load to much or shock it the other direction and you will kill it. This set up moved a three section arm at a good clip, collapsed to extended in about 3 to 5 seconds, we had a lot of sliding friction. Section length was approx 38 inches. This was able to lift the bot onto the bar and hang with out power at the Kettering Kick off.