Prototype 1 Design

Summary of Motor Selection:

Components in the Bay

We currently have the following items in the bay:

• 6x CIM motors
• 6x am-0915 motors (775 motor with a P27 planetary gearbox)
  • Note: The Am-0915 is no longer available off AndyMark, but it should be the exact same as AM-2194 per this post

Motor Options

There are 4 main brushed FRC motors that we can consider using on the arm. CIM, 775pro, BAG and CIM-mini motors. General spec's and motor curves for each motor type are shown below. There are also brushless FRC motors available, but then we need to buy new motor controllers to use them .

CIM Motor (12V)

• Diameter: 2.5" (63.5mm)
• Weight: 2.8lbs (~1.3kg)
• Price: $44.99 CAD

Mini CIM (12V) (similar form factor as regular CIM, can be interchanged across all gears as it has the same mounting interface)

• Diameter: 2.5" (63.5mm)
• Weight: 2.16lbs (~0.98kg)
• Price: $38.99 CAD

775pro (motor standalone) (12V)

• Diameter: 1.744" (44.3mm)
• Weight: 0.8lbs (~0.37kg)
• Price: $25.99 CAD

BAG Motor (12V)

• Diameter: 1.59" (40.4mm)
• Weight: 0.71lbs (~0.32kg)
• Price: $38.99 CAD

Axis 1

Background

Per rough hand calculations, axis 1 has a torque requirement of 14 Nm; adding in a 1.75x safety factor brings it to 24.5 Nm. With the maximum belt reduction supplied by FIRST Versaplanetary timing belt pulley combination, we get a ratio of 3.27:1. Therefore, the axis 1 torque requirement with a safety factor can be brought down to 24.5/3.27=7.49 Nm. However, with each stage of the gearbox being 95% efficient, and assuming 3 stages, this leads to a total efficiency of 85.7%, and a torque requirement of 8.743 Nm.
   

As we can see from this table, the 775 beats other motors in cost while still requiring a low reduction, and having the highest efficiency. In fact, the reduction is so low that it can be pushed to a higher number for a larger torque without worry of the load rating of the gearbox, in order to run the motor at a lower current. 

The small torque requirement is easily achievable by a 775pro with proper gear reductions. Specifically, the max allowable load rating for a 775pro-versaplanetary gearbox combination with a 1/2 hex output shaft is 100:1. By running the 775pro at 13.99A, it can output 0.0708 Nm of torque at 74.462 % effficiency, so the 775pro with a versaplanetary gearbox and belt gear reduction can output a total of 0.0708*100*3.46=24.5Nm of torque.  Almost any gearbox configuration of the 775pro works; it's only a matter of reducing the current load and increasing efficiency.

The cost of the Versaplanetary gearbox only varies with the number of stages, with minimum two being required for our 15.4:1 reduction requirement, and the 775pro-versaplanetary-1/2" hex shaft output combination has a max load rating of 100:1 for two stages. Additionally, the price of the gearbox (assuming buying the base kit) only changes with the number of stages, so it's the most cost efficient to go for a larger reduction than required for the same price, and increase the efficiency of our motor. Thus, a two-stage 50:1 is appropriate and would allow us to run the 775 at max efficiency.



Axis 2

Background

Per rough hand calculations, axis 2 has a torque requirement of 200 Nm. This is the most amount of torque we will require on the robot, so we need a powerful motor and high reduction ratio to lift this load. As such, a two stage reduction on this joint will be necessary. I suggest we use a powerful motor coupled with a planetary gearbox, then use a belt reduction from the output of the planetary gearbox to the joint shaft. While this may create a large/heavy profile for A2, most of the load is located very close to the base of the arm - so it shouldn't contribute to too much higher of a required lifting torque. 

FRC Motor Options

CIM motors offer the highest torque of all motors available from FRC suppliers, and would likely be the best option for A2. There are other motor options available for A2, like the 775pro or bag motors however these all offer much lower torque than the CIM motor. Since speed isn't a necessary requirement for A2, we should prioritize torque and just use a CIM here. Both regular and mini CIM options will be discussed below.

FRC Timing Belts

FRC offers 15mm wide HTD timing belts with a variety of standard and configurable pulleys. All HTD pulley options are cross compatible, as all belts and pulleys have a pitch of 5mm (i checked).

• 60T - 18mm wide VersaPulley (217-3200)
  • PCD = 95.5mm (largest PCD pulley from Vex)
  • Price: $12.99 CAD
  • Weight: 0.22lb (0.1 kg)
  • Material: glass reinforced nylon
  • Output flange to secure shaft
• 18T x 15mm Wide Aluminum Pulley (217-4100)
  • PCD = 28.65mm (smallest PCD pulley from vex)
  • Price: $16.99 CAD
  • Weight: 0.05lb (0.023 kg)
  • Material: aluminum
  • Input: 1/2" hex shaft
• 350mm Pitch Length Timing Belt: 217-3743
  • Price: $15.99 CAD
  • Weight: 0.05lb (0.023kg)
  • PCD Length: 400mm

Timing belt efficiency is generally 98%, so the reduction ratio from this pulley setup would be: 0.98 * (60/18) = 49/15 (~3.27).

If we apply this as our second stage reduction, we can find the reduced output torque for the planetary gearbox: (200Nm)/(49/15) = 61.2245 Nm as planetary gearbox output torque. Lets just round this to 61.25 Nm for simplicity. 

Planetary Gearbox

Next we need to find a planetary gearbox that's capable of converting the motor's torque output to 61.25 Nm. I've been told that our maximum current draw for the motor should be 40A, as that is the max current that the cytrons can handle. The VersaPlanetary is a configurable gearbox capable of offering a high number of ratios. The loading for each stage is described by this guide. Wikipedia says that planetary gears are ~97% efficient per stage , so lets run with 95% stage efficiency to be safe. 0.95^3 = 85.7% efficiency for a 3 stage gearbox. The input torque, max ratio, efficiency and output torque for each motor is listed below.

Note: Max ratio is analyzed for 1/2" hex output shaft

Thus, surprisingly the BAG motor has the highest torque performance which is kind of crazy. I guess they are just condusive to a very high ratio! (Proof Below) Let's refine this number to see current draw at 200 Nm output. 

Source: https://docs.google.com/gview?url=http://link.vex.com/vexpro/pdf/VersaPlanetary-LoadRatings&embedded=true

Total Reduction Ratio (Including Efficiency) = [(60/18)*0.98] * (300*0.857) = 839.86 (lets round to 840).

200 Nm / 840 = 0.238 Nm

At a shaft torque of 0.238 Nm, the BAG motor has a current draw of ~30A and 5930 RPM. The arm will move at ~ 7.06 RPM after reduction. 

To achieve a 1:300 ratio on the VersaPlanetary, we will need 3 stages (1:10, 1:10 and 1:3). A 3 stage versa planetary weighs 0.34 + 2*0.2 = 0.94lbs = 0.43kg.

The total price in CAD is:

• $51.99 for VersaPlanetary v2 Base Kit
• $32.98 for 10:1 VersaPlanetary Gear Kit (x2)
• $32.98 for 3:1 VersaPlanetary Gear Kit (x1)
• $150.93 CAD Total

Other Key Components

VersaPlanetary have a 0.5 in hex shaft output. We will probably need bearings to support the shaft of this gearbox. If we want to be jank, we can 3D print hex to round adapters and slap bushings over the shaft. Or, we could buy the FRC 1/2" hex flanged bearings (which are kind of expensive......)

• We would need 1 minimum to support the planetary shaft, which is $6.99 CAD
• A 12 pack costs $71.99 CAD, so each bearing is ~6 CAD. 
• A bearing weighs 0.058lb (0.0263 kg) 

Total Cost and Weight for FRC Components

After tallying the cost/weight for the BAG motor, timing belt components and bearings:

• Cost (CAD): ~242 CAD
• Weight (kg): 0.923 kg

Axis 3

• Torque required for the axis is 105 Nm
• Torques from the aforementioned torque-speed curves
• 95% efficiency per gearbox assumed
• Belt reduction ratio of 3.27 used (from Austin's work above)
• Calculating total length
  • motor_length + gearbox_length ; each increase in stage has an increase in gearbox length, refer to the length from documentation
  • 2 stage reduction: 60.02mm gearbox
  • 3 stage reduction: 72.72mm gearbox
• Calculating weight:
  • motor_weight + gearbox_weight 
  • Weight of each gear box: 0.34 + 0.2n lb, where n is the number of stages.
  • Convert to kg to be consistent
• Choosing T belt:
  • 60 T large pulley
  • 18 T small pulley
  • Centre distance ~500mm
  • Belt Pitch length: 1197.2mm
  • Closest to belt pitch length: 250T (1250mm)

BAG Motor seems to be the best choice considering length, weight and motor cost. 

Total Cost:

• Motor: $39
• Base kit: $52
• Gearbox Stages: 3 x $33 
• (Versa + Aluminum) 2 Pulleys: $30
• Timing belt (250T): $36
• Total Cost: $256

Axis 4

30Nm torque required. Motor selection same as A5. 

• 775pro motor: $26
• Base kit: $52
• Pulleys: $30
• Timing Belt: $20
• Stages: 2 x $33
• Total Cost: 196

Axis 5

• The target torque for this axis (from the hand calcs) is 30 Nm
• Motor shaft torques are calculated from the links to the motor curves above
• Using Austin's timing belt analysis from above, the best pulley reduction ratio available from FRC is ~3.27. 
• Required reduction assumes a 95% gearbox efficiency
• The weight for each gearbox is 0.34 + 0.2n lb, where n is the number of stages
• Versa lengths are from here

Looking at the chart above, the 775pro is clearly the best option. It is the second best in terms of weight and total length, but this is very close, and it is much less expensive than the other options.

Excluding bearings and such, the total cost, assuming usage of the 775pro, is:

• $26 - motor
• $17 + $13 - pulleys
• $20 - timing belt (120T)
• $52 - VersaPlanetary base kit
• $33 x 2 - VersaPlanetary stages

Total = $194

Usage of am-0915?

Stall torque with pg27 gearbox: 6.67 Nm

Stall torque with 3.27 pulley ratio: 21.81 Nm

An extra 1.4x gear reduction is needed, either with an additional pulley stage or an added gearbox.

Axis 6

Axis 6 requires 18 Nm of torque according to the hand calcs.

Even with one less stage on the CIMs, the 775pro is still clearly the best option. It moves to third place for length, but in my opinion the weight and cost factor override that. The costs for this option are then the same as for A5, excluding the bevel gears and bearings required.

• $26 - motor
• $17 + $13 - pulleys
• $16 - timing belt (90T)
• $52 - VersaPlanetary base kit
• $33 x 2 - VersaPlanetary stages

Total = $190

Usage of am-0915?

Stall torque with pg27 gearbox: 6.67 Nm

Stall torque with 3.27 pulley ratio: 21.81 Nm

If the option with the belt is used, this is a perfect option. Otherwise, an extra 2.7x reduction is needed.