Need Help Understanding Mechanical Advantage of Chain Mechanism

[jmay4096]

Hi guys and girls this my first post! Hope i got it in the right place. I need help understanding the mechanical advantage of this mechanism. The top sprocket is the input power the bottom sprocket is an idler the attachment on the chain is the output. Help!

 

[jmay4096]

More pics of mechanism in gear box. This is an old windengine(windmill). It seems to be 2:1 drive ratio but i just can't wrap my head around it.

 

[Doug Huffman]

Converts rotation of the drive pinion to reciprocation with the stroke from the roller chain. Quite common in aeromotor reciprocating pumps.

Also used is a two sided internally toothed rack on one pinion.

 

[jmay4096]

So it seems the ratio is 2:1 by counting the drive sprocket teeth an the chain links rollers. So is this same as a 15 tooth pinion and 30 ring gear? If so the chain should be like a ring gear and drive sprocket like a pinion?

 

[CWatters]

The top gear rotates and the link carrying the "attachment" travels around the loop of chain raising and lowering the rod which is presumably connected to the load/weight (eg a the load is a vertical force).

The mechanical advantage will vary depending on the position of the link around the loop. Compare these two positions...

1) When the link is at the very top/bottom of the loop the input gear can rotate a small amount (say 10 degrees) without the link moving vertically very much. Most of the movement is horizontal.

2) When the link is on a vertical part of the loop it's further from the centre line of the top pulley so the same 10 degree rotation causes a much greater vertical movement of the rod.

 

[CWatters]

PS: One revolution of the top gear raises or lowers the rod the same amount regardless of the length of the chain. In other words increasing the length of the chain doesn't appear to change the mechanical advantage. (I think).

 

[jmay4096]

I understand the the mechanical motion conversion of the machine its the output of this arrangment that has confused. I can't visually see the mechanical advantage but it must be because the speed ratio between input sprocket and output chain link. Am i wrong to assume that speed ratio difference = advantage? Should the chain be veiwed as an oval shaped roller gear?

 

[Doug Huffman]

The chain length is the length of the stroke, the mechanical advantage is always the radius of the pinion.

I ride a recumbent HPV with about ten feet of chain, adjustable drive pinion (chainwheel) diameter and adjustable driven cogwheel diameter. Roller chain is among the most efficient of jointed mechanisms, amazingly strong and long lived when properly maintained.

 

[jmay4096]

Doug I guess your right thank you Sir. Its just a strange design like i never seen kinda got my sprocket an chain turning lol. Its the fact that the chain link attachment is the output that kinda got me confused.

 

[CWatters]

A recumbent HPV is a slightly different situation. The output on an HPV is rotary where as the output on the pump is linear.

I agree that the mechanical advantage on an HPV will be constant and equal to the radius of the pinion.

Regarding the pump I repeat my comment from above..

The mechanical advantage will vary depending on the position of the link around the loop. Compare these two positions...

1) When the link is at the very top/bottom of the loop the input gear can rotate a small amount (say 10 degrees) without the link moving vertically very much. Most of the movement is horizontal.

2) When the link is on a vertical part of the loop it's further from the centre line of the top pulley so the same 10 degree rotation causes a much greater vertical movement of the rod.

I'll try and post a diagram explaining why later.

 

[CWatters]

Here is a diagram..

If the distance between the pinion gears is large then most of the time the effective radius would be the radius of the pinion.

When they are so close together the mechanical advantage is greater than that for a significant percentage of the time.

The mechanical advantage at the very top or bottom is infinite. The rod doesn't move vertically at all for small angles of pinion rotation in those locations.

 

[jmay4096]

Thanks Cwatters. Any idea how i should calculate the advantage? The thing i can see for sure is that it takes 2 revolutions of both sprockets for the rod to make 1 comlplete path around.

 

[CWatters]

The length of the chain is irrelevant as far as I can see. Changing the length of the chain doesn't effect the force applied to the rod.

As I said before the mechanical advantage varies as the thing rotates so it doesn't have ONE figure for mechanical advantage. Instead there is a range of values. However what usually matters is the lowest value.

If the input torque is a constant (T) then the output force on the rod (F) will be ...

F > T/R

where R is the radius of the pinion (eg what as Doug said).

Rearrange that to give...

F/T > 1/R

So the mechanical advantage is at least 1/R and has units Meters^-1

 

[jmay4096]

Excellent thanks for your time and effort CWatters. Most helpful.