SpiderBall Leg Gears & Gear Housing

This is the key to the entire robot's design. Fitting the gears physically into the space available. Appropriate gears that won't get damaged by overheating, if pushed continuously for 5 mins at full power by a 7.2kW motor. Considering using a drive chain not a gear arrangement.

HPC Gears Ltd extremely competent staff advised that a suitable 5:1 chain drive would require a 3/8in gear-tooth pitch to deal with a 7.2kW motor, and due to the minimum number of teeth required, the large-gear diameter would need to be about 30cm, which is way too big to fit inside a 70cm SpiderBall.

So, they advised a clearance of 1.8mm (!!) between the motor (130mm) and the driveshaft (60mm) on a 5:1 ratio would give a distance between centres of 96.8mm. This gives a ratio of 16mm to 80mm on the radii of the gears, which is 32mm on the small gear, giving a 2.5in (64mm) diam, and 80mm on the large, giving a 6.5in (160mm) diam.

I thought that this was a bit large, and how could it be shrunk, maybe using a 4:1 ratio? Well, no, actually: it goes up :) To achieve that ratio, you need gears of specific sizes, and the closest ones to it give a clearance of 8.75mm. That's a total of 103.75mm between centres. Dividing that up between a 4:1 ratio gives 83.0 to 20.75, which gives gear sizes of 1.63in (41.5mm) diameter for the smaller and 6.53in (166mm) diameter for the larger.

So, funnily enough, a 5:1 gear ratio is probably better. However, a 5:1 gear ratio means that the leg RPM goes down, but it does mean that, to achieve a suitable leg traversal speed, the double-helix engraving needs to be shallower. This has advantages in that a back-kick against the leg will do less damage (think of a Stanley Ratchett screwdriver it has a really shallow double-helix).

Swings and roundabouts...

Gear Ratio Assessement

Let motor speed equal 4,500 RPM (LEM-130 @ 36V). Let motor power equal 7.2kW. Let motor torque equal 5.8Nm. Let gear ratio equal 4:1 Let helix ratio equal 1:1 (45degrees). Let leg diameter equal 35mm. Let the fun begin. ha ha.

Helix Ratio is 1:1 which means that for every revolution, the leg travels 2 * PI distance along.

	Leg Power (N)          = 5.8Nm * 4:1 * 1:1 / (0.035/2)

	                       = 1325.7 N.

	Two Motors (N)         = 1325.7N * 2

	                       = 2651.4 N.

	Escape Velocity (N)    = 200kg * 9.81N/kg

	                       = 1962.0 N.

	Leg RPM                = 4,500 / 4:1 / 1:1
	
	                       = 1,125 RPM.

	Leg travel speed (m/s) = (1,125 / 60) * (PI * 0.035)

	                       = 2.06 m/sec
	
	Two Motors (m/s)       = 4.12 m/sec

So, a 4:1 gear ratio and a 1:1 helix ratio is just about enough, weight-wise. The leg travel speed is adequate: 4.12 m/sec leg travel speed doesn't actually translate into 4.12 m/sec travel speed - that's dependent on the walking mode. I think rolling will be fastest. Any faster a leg travel speed, and the associated reduction in force won't be powerful enough to lift SpiderBall off the ground, on one leg.

Mechanical efficiency will reduce the power to just within acceptable limits. Two motors can generate 2,650 Newtons. The Robot is 200 kg. If the mechanical efficiency is less than 83% (LEM-130s are 90% efficient) then things are not going to be hunky dory... 5:1 or 4.5:1 ratio time...

Let motor speed equal 4,500 RPM (LEM-130 @ 36V). Let motor power equal 7.2kW. Let motor torque equal 5.8Nm. Let gear ratio equal 5:1 Let helix ratio equal 1:1 (45degrees). Let leg diameter equal 35mm. Let the fun begin. ha ha.

Helix Ratio is 1:1 which means that for every revolution, the leg travels 2 * PI distance along.

	Leg Power (N)          = 5.8Nm * 5:1 * 1:1 / (0.035/2)

	                       = 1657.1 N.

	Two Motors (N)         = 1657.1N * 2

	                       = 3314.3 N.

	Escape Velocity (N)    = 200kg * 9.81N/kg

	                       = 1962.0 N.

	Leg RPM                = 4,500 / 5:1 / 1:1
	
	                       = 900 RPM.

	Leg travel speed (m/s) = (900 / 60) * (PI * 0.035)

	                       = 1.65 m/sec
	
	Two Motors (m/s)       = 3.30 m/sec

So, a 5:1 gear ratio and a 1:1 helix ratio is enough enough. Any slower a leg travel speed, and you start to get worryingly slow for Robot Wars.

Mechanical efficiency will reduce the power to within acceptable limits. Two motors can generate 2,650 Newtons. The Robot is 200 kg. We have room for a 65% mechanical efficiency, which I believe is a realistic assessement, given the gear arrangements.

Acceleration Assessement

An assessement needs to be done of leg acceleration and body acceleration.

Let force equal 3314.3 N. Let mechanical efficiency equal 70%. Let mass equal 10kg (just for kicks. *groan*) Let leg be at rest. Let maximum speed equal 3.30 m/sec

	F = ma.
	a = F/m
	
	v*v = u*u + 2as.
	s = v*v / 2a

	v = u + at

	Acceleration = 0.7 * 3314.3 N / 10.0 kg

	             = 331.4 m/sec/sec (eek!)

	Distance     = 3.3*3.3 / (2 * 331.4)

	             = 0.023m

dang that's quick. full speed reached in 2.3cm.

Let force equal 3314.3 N. Let force due to to gravity equal 1962.0 N. Let mechanical efficiency equal 70%. Let mass equal 10kg (just for kicks. *groan*) Let leg be at rest. Let maximum speed equal 3.30 m/sec

	F = ma.
	a = F/m
	
	v = u + at
	t = (v - u) / a

	Acceleration = (0.7 * 3314.3 - 1962.0) N / 10.0 kg

	             = 35.8 m/sec/sec (eek!)

	Time         = 3.3 / 35.8

	             = 0.09 sec

Ramp-up time to 3.3 m/sec velocity is 0.09 seconds, even under a full load. Under 1/10th of a second. *gibber*!

Makes me wish there was space / weight for a LEM-170...