Joint Requirements

Calculations/Background Information

Rough Calculations:

Relevant Pictures:

Axis 1

Axis 2

Axis 3

Axis 4

Axis 5/6

Axis	Permissible Mass for Motor + Gearbox (kg)	Output Ideal RPM	Output No Load Torque, no SF (Nm)	Output No Load Torque, 1.25x SF (Nm)	Output Max Load Torque, no SF (Nm)	Output Max Load Torque, 1.25x SF (Nm)
1	1.1	5-7	3.8	4.7	10	12.5
2	1.5	3-4	61	76	126	158
3	1.3	6-7	18	22.5	55.5	69.3
4	0.8	30	1	1.25	14.1	17.6
5	0.7	30	1	1.25	14.1	17.6
6	0.7	30	1	1.25	14.1	17.6

Note: Permissible mass ratings based off of mass of equivalent actuation components in current arm prototype design. RPM range is based of of teleoperation testing of the prototype arm.

Updated Link Length Arm Calculations

After some investigation, it was realized that the arm can likely be shorter than it how the prototype was designed, as the arm would sit on the chassis of the drivetrain with an approximate 0.35m height above the ground. The proposed new linkage lengths are shown below. If our initial hand calculations used to determine the torques in the table above are accurate (to be validated with testing on 18 Sep 2021 , then we can use these updated requirements for axis 1, 2 and 3:

Axis	Output No Load Torque, no SF (Nm)	Output No Load Torque, 1.25x SF (Nm)	Output Max Load Torque, no SF (Nm)	Output Max Load Torque, 1.25x SF (Nm)
1	2.6	3.25	7.6	9.5
2	44	55	95	119
3	10	12.5	40	50

Updated link lengths do not have any significant changes to the original calcs of axis 4, 5 and 6.

Calculation PDFS:
shortarmcalcs.pdf

Updated Linkage Sketch: (NEED TO ADJUST LINKS FOR BETTER END EFFECTOR LOCATION)

README:

I think these methodology behind these requirements (for both long and short links) were unclear, so just wanted to clarify how I came across these numbers. I reviewed all the mass properties of OTS components for the prototype in SW, and made sure that all material selections were correct. On our prototype arm, I separated the arm into fixed/rigid links and measured the mass and center of mass location of each link. I then used this updated mass/com information to make a point load diagram of the arm and calculated worst case loading scenarios.

For the shortened link calculations, I changed the lengths of linkages to reflect the image above and used the same methodology - measured masses and COM locations of rigid links and used that information to create a point load model of the arm.

Potential Options

This section will review some potential actuation combos that we can use. These were not solutions recommended by sponsors, but options generated by the mechanical team. The following factors listed below are the critical success factors for potential actuation combination options.

Low total cost
Low total mass profile
Reliability throughout range of operating conditions
Low Backlash
Technical Feasibility

Option A (24V Motors)

Axis 1 - Option A

Motor: https://us.nanotec.com/products/2152-db59l024035r-a

Continuous rated torque of 0.47 Nm
$173 CAD with no discount (although we should contact this company and ask for sponsorship before buying
rated speed of 3500 RPM
Weighs 0.72kg
Currently in stock 16 Sep 2021

Gearbox: https://us.nanotec.com/products/9903-gp56-n2-35-sr

35 ratio → ~16 Nm of torque on output when operating at motors continuous torque rating which exceeds our requirement at a 12.5x SF
Weighs 0.78kg
Easily configurable with selected gearbox (according to manufacturer website, although would need to confirm that no additional costs are required to mate components)
Currently in stock 16 Sep 2021
Maximum backlash of 19 arcmin according to manufacturer (0.3º)
$251 CAD with no discount (although we should contact this company and ask for sponsorship before buying

Overall Pros

Fulfills and exceeds our torque requirement
Relatively low cost option, even without any discounts ($424 CAD)
Potentially we could buy an encoder which mates to the motor on the back of the encoder for easy integration, although this is not necessary
Very low backlash
All parts are currently in stock, need to confirm lead times though

Overall Cons

Exceeds our mass requirement (total mass combination mass of ~ 1.51kg), however this will not be on-joint mass (mass will be mounted to turntable) so it will not affect the performance requirements of other motors
Somewhat bulky. If we use an inline option, the length of the configuration will be approximately 150mm. We would likely need to attach this to a belt drive off axis with respect to A1, as if we mount it directly underneath the turntable we will lose a considerable amount of chassis clearance
Joint will be backdriveable, although we should not see too many loads that will move this arm
Will operate at approximate 100RPM after gear ratio. Further speed control is required via PWM to reduce the motor's speed for a reasonable teleop range.

Notes on Other Options: We can also use the 45mm maxon + harmonic drive option here. however, I figured that might be expensive and not really worth investing in.

Second Note: Why not use the maxon gear heads and maxon motors here? Well, this option is cheaper. The additional mass does not influence other joint requirements. And, it has significantly low backlash! We can stick with maxon if need be though.

Axis 2 - Option A

Motor: https://www.maxongroup.us/maxon/view/product/motor/ecmotor/ecflat/ecflat45/651614?etcc_cu=onsite&etcc_med=Header%20Suche&etcc_cmp=mit%20Ergebnis&etcc_ctv=Layer&query=651614

Continuous rated torque of 0.134 Nm
~170 CAD after electromate discount, ~235 CAD full price
Weighs 0.15kg
Rated speed of 5600 rpm
Currently in stock 16 Sep 2021

Gearbox (Stage 1): https://www.maxongroup.us/maxon/view/product/gear/planetary/gp42/260552

36 ratio → ~ 4.86 Nm of torque when operating at continuous torque limit of motor (not accounting for efficiencies).
Costs ~437 CAD without educational discount (need to confirm with electromate if discounts are available for this product)
Backlash of 0.8 degree
Max continuous torque of 7.5Nm, permissible intermittent torque up to 11.3 Nm
Can purchase directly mated to the current maxon motor
Unknown if currently in stock, need to confirm with electromate
Weights 0.36kg

Gearbox (Stage 2):

would use couple a worm and worm gear to planetary gearbox output. Will do more research soon, but this should be very doable

Axis 3 - Option A

Motor: https://www.maxongroup.us/maxon/view/product/motor/ecmotor/ecflat/ecflat45/651614?etcc_cu=onsite&etcc_med=Header%20Suche&etcc_cmp=mit%20Ergebnis&etcc_ctv=Layer&query=651614

Continuous rated torque of 0.134 Nm
~170 CAD after electromate discount, ~235 CAD full price
Weighs 0.15kg
Rated speed of 5600 rpm
Currently in stock 16 Sep 2021

Gearbox: https://www.harmonicdrive.net/products/gear-units/gear-units/csg-2uh/csg-17-120-2uh

120 ratio → ~16.2 Nm of torque on output when operating at continuous torque rating of motor
Weighs 0.68 kg
1.5 arc min of backlash (effectively 0 backlash)
$1345 CAD after educational discount (full price cost is actually unknown)
Easy to integrate with selected motor according to electromate (need specifics on this)
Rated L10 torque of 31 Nm, average torque limit of 51 Nm, repeated torque limit of 70 Nm, momentary peak toruqe limit of 112 Nm
back driving torque of 3.9 Nm
Currently in stock 16 Sep 2021

Overall Pros:

When operating at motor's continuous torque limit rating, gearbox torque exceeds no load arm torque requirement
Very low combination weight (~0.83kg)
Effectively 0 backlash
Very low profile option (super flat, expected length of ~75mm without encoder considerations.
Gearbox output is flange type, so should be relatively easy to couple to a joint

Overall Cons:

Arm will naturally backdrive when horizontal, as no load torque exceeds the back driving torque,
EXPENSIVE (combination will be 1515 CAD without shipping)
May potentially require other components required for integration (need to confirm with maxon/electromate)
Operates at 47 rpm at continuous torque, so will need duty cycle to regulate motor speed to a reasonable teleoperation range

Arm should be able to lift the maximum required load (of shortened arm config). 50 Nm of torque is within rated operating limits of the gearbox and requires 0.416Nm of torque from the motor. The stall torque of the motor is 1.69Nm, so this is well below stall. 0.416Nm of torque from the motor is approximately 3x higher than the continuous rated torque of the motor. According to Maxon BLDC Operation Fundamentals, typically at ambient conditions motors can supply 2.5x the continuous torque limit for approximately the thermal time constant of the motor without worrying about any continuous damages to the windings. I think it should be safe to say that we can expect to power the motor with 0.416Nm at half the thermal time constant of the winding which is a continuous operation time of about 20seconds. I pretty much pulled this number out of thin air though. This is like a pro and a con, at the same time, not necessarily a straight pro.

Axis 4/5/6 - Option A

Motor: https://www.maxongroup.us/maxon/view/product/motor/ecmotor/ecflat/ecflat45/651614?etcc_cu=onsite&etcc_med=Header%20Suche&etcc_cmp=mit%20Ergebnis&etcc_ctv=Layer&query=651614

Continuous rated torque of 0.134 Nm
~170 CAD after electromate discount, ~235 CAD full price
Weighs 0.15kg
Rated speed of 5600 rpm
Currently in stock 16 Sep 2021

Gearbox: https://www.maxongroup.us/maxon/view/product/gear/planetary/gp42/203127

126 ratio → ~17 Nm of torque when operating at continuous torque limit of motor
Weighs 0.46kg
Costs ~465 CAD without educational discount (need to confirm with electromate if discounts are available for this product)
Backlash of 1 degree
Max continuous torque of 15Nm, permissible intermittent torque up to 22 Nm
Can purchase directly mated to the current maxon motor
Unknown if currently in stock, need to confirm with electromate
Backdriving torque currently unknown, although probably similar to the vexpro gearboxes on the prototype. Axis 4,5 and 6 all do not backdrive on prototype, so it may be reasonable to assume that these gearboxes will also not backdrive as both are 3 stage planetary gearboxes

Overall Pros:

Motor can actually operate at lower torques (as all torque operations lower than the max continuous torque are permissible for max permissible torque) and thus recruit less current
Gearbox is rated for all loads that will likely be seen on these motors (if hand calcs are close to tested values)
Probably won't backdrive...
Very low weight per axis (0.61kg)
After reduction, operates at approximately 45 RPM. This is close to our ideal range, so will only need need slight speed control on the motors
Moderately compact (expected length of 100mm)

Overall Cons:

Moderate overall expenses (~635 CAD per combination, although there may be some savings from electromate)
1º of backlash on gearboxes, but these have smaller lever arms so may not be a huge issue
need to confirm gearhead availability with electromate

Summary Table - Option A

Approximate Actual Team Cost (applied a preemptive 25% discount on maxon gearheads as motor was discounted by 25%): 3500 CAD

URC Cost (just assumed actual harmonic gearbox cost was 1800 CAD, need to confirm true cost with electromate): 4520 CAD

Axis	Mass	Backlash	Backdriveable	Motor Cost	Gearbox Cost	Total Cost	Motor Operating Range at No Load	Motor Operating Range at Max Load	Integration Feasibility
1	1.51kg	0.3º	Yes	$173	$251	$424	Within Continuous Operation Range of Motor	Within Continuous Operation Range of Motor	High
2			No	$170	$437 +	$607
3	0.83kg	0	Yes	$170	$1345 CAD		Within Continuous Operation Range of Motor (for shortened link length arm)	Within Short Term Operation Range of Motor, likely can be operated for ~ half of thermal winding time constant	High
4/5/6	0.61kg	1º	Yes	$170 ea.	$465 ea.	$635 ea.	Within continuous operation range of motor	Within continuous operation range of motor	High

Note: Integration is high for maxon motor/gearhead or the nanotech motor/gearhead as these components are configurable combinations on supplier website. Additionally, according to actuator sponsor the selected maxon motor and harmonic gear for A3 easily mate to eachother.

Decision Matrix - Excel Sheet

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