Axe mechanism

[nick]

Axe mechanism

The analytic formula for energy/distance for a mass m moving under constant power P is

Energy at distance s=(9/8 M P2 s2)1/3
so...dividing by P
Time at distance s=(9/8 M P-1 s2)1/3

This is a only slightly quicker swing than in Johns formula, since this is for perfect gearing throughout the stroke, and there are

several complicating factors, you can expect the real swing to be a bit slower and achieve slightly lower energy.

[Guest]

Axe mechanism

Great, thats lots of help. Shame Im too close to a big comp to redesign it for a more efficiant gear ratio.
One thing is John said I need a 10:1 reduction using 2500rpm from the motor, but an EV at 24V is rated at 4480 at no load. Is there something else Im missing (wouldnt surprise me).
Also Im intersted in the snail cam on Beta. Im not quite sure how to calculate the shape of the cam. This is just a guess but I had a go. I used the time for the axe to swing as you showed me, broke down the equation for power and rearranged with respect to acceleration (power = force x velocity, but this doesnt feel right) so I had a = (p*t)/(m*s). I used pi for s as I wanted the answer to be repesented in angular acceleration measured in radians (pi = 180 degrees). Once I had the acceleration I multiplied it to the time to get the angular velocity at the end of the swing. I converted it to rpm and used it to find the best gear ratio. I used this as the gearing on one end of the cam. For the other end I decided to use it and the average gearing to find the other end so the average radius of the cam is equal to the average gearing. For one set of sums I ended with 13.5:1 for the average gearing, 7.7:1 at one end of the cam and 19.3:1 at the other.
Am I wasting my lunch breaks here?

[Guest]

Axe mechanism

The no load speed of an EV on 24V is 5000 rpm, so the speed at which peak power is produced is 2500 rpm.

[nick]

Axe mechanism

What you might not have realized(?) is that you only get peak power for the system at around half the no-load speed, when you are very close to the no-load speed the motor is taking hardly any current and generating hardly any power so you want to avoid going near it. Its exactly the same in terms of power output if your very close to stall except your taking tons of current, and its generating tons of heat....which is bad.

Thats why were determined to stay somewhere around 2500rpm, maybe just over to reduce the amount of current flowing through the system. EV warriors are often timed so they run quicker in one direction than another, or some such. This is a bad thing if you intend to run it both ways, and I intend to ignore it too. (Theres also some contention on the no-load speed of the EV, or rather what it would be without friction, this might be what you are at issue with, 4480rpm versus 5000rpm?)


The actual energy gain using snail cams over the best fixed value gear ratio is in (the simplest)theory fairly small, it has a slightly bigger affect on swing time. However it tortures the motor and batteries with the very high currents over too much of the stroke if you go for peak energy in a fixed ratio system.

If you dont saturate the motors armature and the cells hold up for long enough under this abuse, you can get within about 7% of the max amount of energy a changing gear ratio system could provide. Those two things you cant really be sure of, so realistically your going to probably lose more than 10%. But the machines endurance should be a lot better if you use cams to make it more efficient.


I think John worked out an overall fixed ratio of about ~9:1 is about right(we dont know the length of the shaft so were guessing 0.3m from centre of pivot to centre of hammer head). That would mean a good cam would probably start of at about 20:1 and end at 6:1. When you build it you may come up against a problem fitting such a big gear change in the space available, then you just cut back until everything fits.

Your figures arent that far off these, so I doubt your lunchtime was completely spent in vain. Thats for absolute peak power, generally you want to keep just on the lower current side of peak power, you only lose about ten percent power but your power wont drop off abnormally quickly as you keep pounding your opponent.

Your approximate expression for acceleration is ok. If you chose m to be shaft_length*shaft_length*head_mass when s is in radians. I assume you did that, because your numbers do work. Using the average gear ratio as a pivot to work out the high gear ratio end is rather clever, it might not be totally rigorous but it worked. Thankfully a lot of the calculations involving the gear ratios seem to be fairly forgiving anyway.


The actual designing of the cams to have the right gear ratio is made more complicated because of the angle of the chain is changing and so forth, luckily you dont have to get it very accurate if your only interested in energy.

Back to that constant power equation...its more accurate when your using cams as then the power is much more constant.
Energy = (9/8 M P2 s2)1/3
so speed= (2 M-1 Energy)1/2
[at which point a horrible thought occurs]
Speed= (9/1/6 (2/M)1/2 M1/6 P2/6 s2/6
after almost losing the will to live....
Speed = (3 M-1 P s)1/3

260 is about half the motor no-load speed in radians per second...its when the motor is around peak power. You could go a bit higher so things are a bit more efficient with only a small reduction in power eg. 350 radians per second. You have to change the power in the formula accordingly.

ideal ratio at distance s=~260*shaft_length/linear_head_speed
so ideal ratio at distance s=~260*shaft_length * (3 M-1 P s)-1/3

If x is the angle in radians of the hammer, where x=0 is the start condition of the shaft you get this

ideal ratio at angle x=260*(1/3 * shaft_length2 M P-1 x-1)1/3
Plugging in shaft_length=0.3m (pivot centre to hammerhead centre) M=1.0Kg P=750Watts (optimistic...no friction)
gives an ideal ratio at x=3.14 (end of stroke) of a shade over 6:1
Obviously as you get closer and closer to the start of the swing the ideal gear ratio becomes infinite. Thankfully its not necessary to actually go this far, and big enough is....enough.
At a tenth that angle x=0.314, the ideal ratio is 101/3 times bigger...or about 13:1 so by the time your at 18:1 or more you are only left hurting a small amount of beginning of the stroke.

[glen]

Axe mechanism

whats the general opinion on spring powered axes? is it better to just go with an all electric one in the first instance or what? (id like to keep away from pneumatics big time).

ive started on a little axe robot now () and i was thinking of using this huge beast of a windscreen wiper motor (http://robowars.org/forum/album_pic.php?pic_id=574http://robowars.org/forum/album_pic.php?pic_id=574) to wind back the axe and compress the springs in my design, but would it be easier and work just as well to use a couple of linkages and power the axe straight from the gearbox?

i doubt the motor itself is lacking in power. its like twice the size of a normal windscreen wiper motor but im still not sure if the plastic gear inside the gearbox would strip the teeth off even with a linkage or two on it.

thanks in advance

[knightrous]

Axe mechanism

Glen, talk to me on msn, I have a very very simple design for you that should work well

[maddox]

Axe mechanism

Glen, Im currently building an hydraulic axe.
Also possible for an feather, or a simular system powered by a linac.

Mail me for more info.

[psychostorm]

Axe mechanism

Hate to revive an old thread but could anyone help me figure out a gear ratio for an motor powered axe?

(motor powered purely due to my lack of experience with pneumatics, you understand.)

The Axe Im planning has a roughly 700G head, 0.3M handle and will probably be driven by a 24V Gold motor.

Ive tried the formula but its making as much sense to me as an in-flight magazine produced by air belgium...

Anyone fancy lending me a hand?

[ewan]

Axe mechanism

Do you want it to have enough torque to allow self-righting?

[nick]

Axe mechanism

Hmm, maybe about 13:1.
Its also roughly the number you get if you calculate the ideal gear ratio at the 90 degree position for a motor developing about 120watts at 2700RPM.

[psychostorm]

Axe mechanism

Nick, 90 Degree postion. you mean falling from vertical, the original Xterminator style?
Not what I had planned. 180 degree.

and yes, I need this Axe to self right. without going 180 degrees it cannot self right and theres nowhere else in my design (on profile) for a schrimech.

[ewan]

Axe mechanism

The figures arent too good for using a gold im afraid. Youd only get about 11mph speed on the axe if the arm is 320mm long and has a tip torque of 13kg (using 18:1 ratio). It really depends on the robot shape to if it will be able to self-right at say 10kg torque at the tip.

[psychostorm]

Axe mechanism

I knew that from the start, I just didnt want to admit it.

It would be better if I used Pneumatics but I have no idea how to implement them into a feather.

[ewan]

Axe mechanism

The figures for an old-style 18v DeWalt drill motor are far better though (available from the US - http://www.robotcombat.comwww.robotcombat.com or http://www.teamdelta.com/products/prod5.htmwww.teamdelta.com/products/prod5.htm). If you brought the matching gearbox (maybe the kit from team delta which includes a mount) then you could get 34mph hammer speed with 14kg tip torque if you use it in low gear geared up by 1:2.

[nick]

Axe mechanism

Sorry Ceri, I meant if you have an axe with a 180 degree swing. Using the same ratio as a variable ratio axe system should have at about 90 degrees gives you a fairly decent ratio for a fixed ratio system.
Im afraid Ewans right about the power, a DeWalt or EV warrior is a lot more powerful but of course you have to up-rate everything else to get the best out of it.
How much torque you need to self-right is fairly dependant on robot length, the shorter it is the easier it gets.
Going up to 36 volts from 24 increases the available energy by about 70% if that is an option.