Human Inertia (Weight Distribution in Design)

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So, at-a-glance the key specs of this servo with a 1:3 gear down are;
Max Torque: 76.5Nm
Max Speed: 0.36s/60*
Range of Travel: 0-100*
Max Rpm (@24v): 27.6
Control Accuracy: 0.1*
Weight: 375g
Dims: 95x60x110mm
Price: £57.87p

Now considering & aiming towards Standardised Model of a human,
Average Adult Size (male)
Height: 1770mm
Width (Arms Ext): 1800mm
Weight: 73kg
Foot-to-Hip Length: 920mm
Foot Width: 75mm
Cog: 58% of Max height (above floor)

and,

A Breakdown of the key DOF's;
Head/Neck: x3
Torso: x2 (1x each side)
Shoulders: x6 (3x each)
Elbows: x2 (1x each)
Hips: x6 (3x each)
Knees: x2 (1x each)
Ankles: x4 (2x each)
Feet: x2 (1x each)
Total DOF's: 27

and,

The proportional weight of regions,
Torso: 48.3%
Thigh/Upper Leg: 21% (10.5% x2)
Head/Neck: 7.1%
Lower Leg: 9% (4.5% x2)
Upper Arm: 6.6% (3.3% x2)
Lower Arm: 3.8% (1.9% x2)
Foot: 3% (1.5% x2)
Hand: 1.2% (0.6% x2)
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Using the linked servo in all heavy duty/Torque hungry DOF's, complimented with heavy duty hobby servo's for lighter duty DOF our servo weight per region looks like this;

Servo weight per DOF/region
Head/Neck: x3 0.3kg
Torso: x2 (1x each side) 0.75kg
Shoulders: x6 (3x each) 2kg
Elbows: x2 (1x each) 0.2kg
Hips: x6 (3x each) 2.25kg
Knees: x2 (1x each) 0.75Kg
Ankles: x4 (2x each) 1.5kg
Feet: x2 (1x each) 0.75kg
Total DOF's: 27 8.5kg

Using CHARLI-2 as an initial reference, we know that 68.1% of total weight is structural & light on-board electronics (non-servo?).
This leaves 31.9% in CHARLI-2's case exclusively dynamixel servo weight.
In this instance we know the complete (27x Servo's) weight totals 8.5kg. Treating this as accounting for 31.9% (as in CHARLI-2's case), we can deduce that the remaining 68.1% of structural/light electronics weight will account for 18.5kg, so

Total Servo Weight: 8.5kg
Total Structural Weight: 18.5kg
Total AUW: 27.2kg

With an estimated AUW we now have a baseline to begin breaking down mechanical specs further using the proportional weight of humans as a benchmark.

AllUpWeight/Region (of 27.2kg),
Torso: 13.14kg (48.3%)
Thighs: 5.71kg (21%)
Head/Neck: 1.93kg (7.1%)
Lower Legs: 2.45kg (9%)
Upper Arms: 1.8kg (6.6%)
Lower Arms: 1.36kg (5%)
Feet: 0.82kg (3%)
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At a glance, we can see that direct-mount of Servo's in certain regions is not possible if we are to maintain a) a low centre of gravity, b) evenly distributed mass in line with human proportions, and subsequently c) the evenly distributed mass provides an efficient & humanlike moment of inertia.

Nonetheless, its a worthwhile task to view the figures assuming all Servo's are mounted in a direct-drive style, this will allow us imagine ways in which mass may need to be redistributed.

Again, for the purposes of this analysis we will assume our humanoid has a total weight of 27.2kg. Four of the shoulder servo's are have been added to the Torso Region with remaining two shoulder servo's added to Upper Arm Regions.

Region AUW / Servo/W / AUW-S/W
Torso: 13.14kg 2.09kg 11.05kg
Thighs: 5.71kg 2.25kg 3.46kg
Head: 1.93kg 0.3kg 1.63kg
L.Legs: 2.45kg 2.25kg 0.2kg
U.Arms: 1.8kg 0.66kg 1.14kg
L.Arms: 1.36kg 0.2kg 1.16kg
Feet: 0.82kg 0.75kg 0.07kg
Totals: 27.21kg 8.5kg 18.71kg
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Another way to digest this is to view how much wiggle room for weight there is for each regions structure & associated electronics,

Region Avail Struct kg Local Servo
Torso: 11.05kg 6x
Thigh (Each): 1.73kg 3x
Head: 1.63kg 3x
L.Leg(Each): 0.10kg 3x
U.Arm(Each): 0.57kg 2x
L.Arm(Each): 0.58kg 1x
Foot(Each): 0.035kg 1x
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As predicted, its clear to see by direct-mounting servo's, for certain DOF's & Regions the little remaining weight allowance for structural part of those Regions, makes it impossible mount actuators in this way. First we'll identify those impractical Regions, and then we can assess how to overcome those limitations. After we can redraft a new weight distribution table to confirm we're within acceptable specifications.

Region Avail/kgs Practical Servos
Torso: 11.05kg Yes 6x
Thigh: 1.73kg Yes 3x
Head: 1.63kg Yes 3x
L.Leg: 0.10kg No 3x
U.Arm: 0.57kg Tight 2x
L.Arm: 0.58kg Tight 1x
Foot: 0.035kg No 1x

We can clearly see that direct-drive of the joints is not practical in most cases.
There is however, room for manoeuvre.
• Some servo's can be redistributed to the perimeters of the torso (although, every attempt should be made to keep this additional weight as near to the waist as possible, remembering the human COG is typically 58% of max height measured from floor level-up).
•In cases where the servo it too far (an extremity) from the torso region to relocate to this area, we can minimise & address the effects of these kinds of issues in the design stage.
•we can utilise 'distance friendly' drives (belts, pulleys, chains etc.
•Appying passive/semi-passive joint solutions in place of active servo joint control where suitable.
•Use if alternative lighter servo's where torque requirements aren't demanding.

Next section will give brief description of proposed solution before proceeding to how impact of these solutions.
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Key areas where servo weight needs reduced, redistributed or eliminated are;
•Feet
•Lower Legs
•Lower Arms
•Upper Arms
These areas will be highlighted in Bold text to keep our attention in those areas.


Reminder initial of parameters,
AllUpWeight/Region (of 27.2kg),
Torso: 13.14kg (48.3%)
Thighs: 5.71kg (21%)
Head/Neck: 1.93kg (7.1%)
Lower Legs: 2.45kg (9%)
Upper Arms: 1.8kg (6.6%)
Lower Arms: 1.36kg (5%)
Feet: 0.82kg (3%)


Servo weight per DOF/region
Head/Neck: x3* 0.21kg
Torso: x2 (1x each side) 0.7kg
Shoulders: x6 (3x each)* 1.5kg
Elbows: x2 (1x each) * 0.15kg
Hips: x6 (3x each) 2.1kg
Knees: x2 (1x each) 0.7Kg
Ankles: x4 (2x each) 1.4kg
Feet: x2 (1x each) (Passive) n/a
Total DOF's: 27 Total: 6.76kg

(* indicates the use or inclusion of lighter 70g hobby servo's)

Using 70g hobby servo's in the elbows, the rotation joint of the shoulders, the 3x dof's of head, and the removal of one dof in feet (replaced with semi-passive dof) has achieved a reduction in the total servo weight of 1.74kg (or Over 20%).

The next step is in managing the redistribution of servo's where possible.
The redistribution looks like so;

Dof Servo Relocated to Kg Moved
Ankles Below Knee 1.4kg
Knees Upper thigh 0.7kg
Hips Bottom Torso 2.1kg
L.Arms Mid Upper Arm 0.15kg
U.Arms Out/InsideShoulder 0.15/1.35
Head Neck/Top Torso 0.21kg
Torso Abs level of Torso 0.7kg
Feet n/a (Passive) n/a

We can now transfer the newly redistributed weight values into a table to see if there's adequate enough empty weight in each region to build robust structure/body.

Region AUW / Servo/W / AUW-S/W
Torso: 13.14kg 4.27kg 8.87kg
Thighs: 5.7kg 0.7kg 5kg
Head: 1.93kg n/a 1.93kg
L.Legs: 2.45kg 1.4kg 1.05kg
U.Arms: 1.8kg 0.3kg 1.5kg
L.Arms: 1.36kg n/a 1.36kg
Feet: 0.82kg n/a 0.82kg
Totals: 27.2kg 6.67kg 20.53kg

Now we're looking a lot more healthy in our margins for structural weight, and you'd be forgiven for thinking the basic foundation of our work is complete, however if we remember the 'servo to structural weight' ratio we began with (used as a benchmark to estimate the appropriate weight, in leu of a 'Standardised Model'), based on the CHARLI-2's ratio of 31.9-68.1% (servo to structural weight). When we encountered weight issues in our initial plans, we reduced the total servo weight by over 20% to overcome that hurdle, but that means our ratio should look like this now;
Total Servo Weight: 6.67kg
Total Structural Weight: 14.23kg
Total AUW: 20.9kg

The question arises, how significant and/or beneficial is it to keep this ratio? As we stand now, our 'servo to structural' weight (6.67kg-20.53kg) ratio is 24.5%-75.5%.

Personally, I don't see any great importance in the 'Servo-To-Structural Weight' Ratio at this time, if there is a relationship I'd like to uncover & document how these values interact with one another.

Out of curiosity, and because I want to see if i can achieve a CHARLI-2 ratio with still enough meat-on-the-bones' to build the structure I'll through the numbers up;

Region AUW / Servo/W / AUW-S/W
Torso: 10.1kg 4.27kg 5.83kg
Thighs: 4.39kg 0.7kg 3.69kg
Head: 1.48kg n/a 1.48kg
L.Legs: 1.88kg 1.4kg 0.44kg
U.Arms: 1.38kg 0.3kg 1.08kg
L.Arms: 1.05kg n/a 1.05kg
Feet: 0.63kg n/a 0.63kg
Totals: 20.9kg 6.67kg 14.23kg

Very, very tight, however achievable,..