# Need a mechanism for reciprocating motion

1. Jul 23, 2011

### SteamBC

I'm developing an automatic spray-paint shaking machine in order to achieve very well mixed paint for a big project. Since I'm using stone textured paint with lots of fibers and "Stuff" floating around in it, I'd like to go above and beyond in the shaking.

Simply put, I want to roughly emulate the human arm shaking a can of spray paint.

My only concern is achieving reciprocating motion that doesn't slow down too much near the end and beginning of the strokes. Sorry, as you can tell I'm not formally trained.

The usual mechanisms of which I'm aware tend to stroke faster in the middle and slow down toward each direction change, which seems counter-productive to my purpose, although it would certain work.

Is there any kind of mechanism that will provide constant velocity? The speed I'm looking for is slightly faster than the average person shaking a can of paint. Of course, the weight of the paint and the carriage will be a factor in terms of inertia.

Actually, as I'm typing this I'm thinking of a gear with teeth on one side only, rotating and alternately meshing with two parallel racks, each rack on opposite sides of the gear. That might be my solution, but all other ideas would be appreciated.

Last edited: Jul 23, 2011
2. Jul 23, 2011

### jambaugh

Remember that at the exact end of each stroke you must get to zero speed.
The sharper you make the change, the higher the forces involved.

Here's a suggestion, pad the can and put it in a dryer and let it tumble or some equivalent but more controlled analogue...

You can use nested motorized wheels driving a rod along a track to create any type of motion you like. Consider that what you are describing, in terms of position as a function of time, is a http://en.wikipedia.org/wiki/Triangle_wave" [Broken].

Looking at its Fourier expansion:
$$x(t) \propto \sin(\omega t) - \frac{1}{9}\sin(3\omega t) + \frac{1}{25}\sin(5\omega t) - \ldots .$$
So start with a wheel or radius R rotating at one speed in a cw direction. Attach a wheel of radius R/9 at the edge of the first wheel and rotating 3 times faster but in the opposite ccw direction. Then add a wheel of radius R/25 rotating 5 times faster in the cw direction and so on as far as your perseverance and resources allow. To the last wheel attach a push rod connected to the sliding track holding your spray can.

Two wheels is probably all you can implement easily, say 27 inches radius and the 2nd wheel 3 inches in radius. You can probably figure out a gear system to turn the 2nd wheel 3 times faster than the 1st so you don't have to mess with a 2nd motor and worry about speed control plus wiring.

Hmmm... OK Make the 2nd wheel 1/3 the radius of the first wheel, or to be precise 1/3 the distance from its axis to the axis of the first wheel. Make a cylinder (radius 1+1/3) so that the 2nd wheel rolls along the inside, (cut teeth if you like to make it a cog and sprocket). Then attach the push rod to the 2nd wheel 1/3 of its radius out (1/3 of 1/3 = 1/9 the big wheel's radius). That should do it.
[EDIT: Here's a rough diagram...

I've attached a graph of the vertical displacement as a function of angle.
END EDIT]

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3. Jul 24, 2011

### SteamBC

LOL, I love the dryer idea. It would work, but naturally I'm looking to make something one step up in elegance and to learn something in the bargain.

I fully understand the graph and the motion you're describing, but I'm having a little trouble envisioning the actual mechanism you're describing.

When I think of the term "nested" I think of one wheel being actually inside another, but I don't think that's where you're going here. Do you mean "stacked"?

Any chance of getting you to dumb the description down to my level? I'm not sure how the wheels are oriented relative to each other and to the pushrod, and how the rod would be attached to the rod.

4. Jul 24, 2011

### SteamBC

Oops, you made your edit while I was typing my response. I'll study it carefully before replying.

Again, I genuinely appreciate your time!!

5. Jul 24, 2011

### SteamBC

I'm not clear as to the function of the blue wheel other than to rotate the red gear, which is what seems to be supplying the reciprocating motion. It seems in your diagram that the blue wheel's provided reciprocation is incidental and slow compared to the red which is actually doing the useful work.

I guess my question is, why is the blue wheel needed at all if the red gear is providing 3X the reciprocating force?

I'm sure I'm missing something painfully obvious here. Perhaps I should try to prototype it in Algodoo in order to observe the actual effect.

6. Jul 24, 2011

### Unrest

How about let it bounce back and forth off elastic end-stops. You could have some simple control system or a clever mechanical widget to engage a motor only during half the cycle to give it a boost in the same direction each time.

Or perhaps one of the end stops is an actuator that kicks the can away when it hits it. Like a bumper in a pinball machine.

7. Jul 25, 2011

### jambaugh

As the blue gear turns it moves the red gear in a circle so if the red gear were just glued on you'd get a sinusoidal action with amplitude = blue radius + 1/3 red radius. If you had the red gear with an independent motor rotating it then you'd get the sum of two arbitrary sinusoidal motions, one with amplitude= blue radius, the other with amplitude= 1/3red radius, and with frequencies determined by the motor speeds. (1/3 red radius since arm is attached 1/3 from center)

The outer sprocket drives the red gear at 3 times the speed of the blue gear and in opposite direction to get the fourier terms I provided in the earlier post.

The coupling of the two motions produces the 2nd order approximation of a triangular wave which is what you were aiming at: triangular wave = constant motion between turns.

You could add a third gear to the red one to get the next term in the Fourier expansion but as you can see by the graph you get pretty darn good approximation with just the two.

For prototyping I suggest foam core board. For implementation I suggest a heavy solid blue wheel to act as a flywheel so as to get more uniform motion.

8. Jul 25, 2011

### DickL

Consider using the mechanism that Mercedes uses for their single wiper blade systems. It is similar to your original suggestion of a gear running against a rack. Rather than a gear with teeth only on apart of the gear, it is a normal spur gear. The rack has its teeth running completely around a slot that is somewhat wider than the diameter of the gear. The gear runs along the rack, and changes directions as it runs around the end of the rack and starts back on the other side.