Asymmetric Ross Linkage

[Gillybob]

I am designing my first Stirling engine and am going for a Gamma type and I am intending to use a Ross Linkage.

I have been reading Roy Darlingtons book in which on page 30 he outlines the sizing recomendations for a Stirling engine which are:

Power piston diameter = 2x sweep
Displacer swept volume = 1.5 x power piston swept volume
Displacer swept volume = 1/3 total volume
Displacer cylinder length = 3x diameter

On the basis that I want to measure twice and cut once so to speak, I am trying to dome some sums before I start drawing. In order to comply with the dimensions above, everything can be described in terms of the power piston diameter:

So if we take the diameter of the power piston as “d”
Sweep = d/2
Power piston swept volume = pi*d^2/4 *d/2 = pi*d^3/8
Displacer Swept volume = 1.5*pi*d^3/8 or 3*pi*d^3/16
Total volume of displacer cylinder = 9*pi*d^3/16

If we take the diameter of the displacer as “D” then
the volume of the displacer cylinder = pi*D^2/4*3D = 9*pi*d^3/16
Therefore D=0.909*d
The length of the displacer =2.725*d


The crux of all this is that the sweep of the Displacer piston will be 0.908*d whilst the power piston will be 0.5*d. This means that the displacer needs to have 1.82* the movement of the power piston.

All the images that I have seen of Ross Linkages show a symetrical arrangement, but this will not allow for the 1.82 variation in movement. I have put together a spread sheat to calculate the dimensions that I will require for this asymmetrical arrangement and think that it should work but I would be interested in what anybody else thinks.

The spreadsheet can be found below if you are interested.

https://1drv.ms/x/s!AnMn0rJaalvJ-GWjfOTzfe2qIXh7

[Ian S C]

The only reason you have only seen symmetrically arranged linkages is that they are usually on an ALPHA motor that works on a 1:1 ratio, there is no reason not to use the linkage on a GAMA motor.
Here is a view of my ALPHA motor before I modified it for the second time, still got to get a new photo of it.
The latest mod done was to remove the side arm that locates the yoke, and replacing it with a vertical slot, and a little roller. I also had to do a repair job on the crankshaft, so I increased the stroke by 4 mm. There is now less that 1 mm clearance for the big ends and the bottom of the crankcase. In the past I replaced the water cooling jackets, and made an aluminium cylinder head to replace the steel one it started with.
Ian S C
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Test 008 (640x480).jpg (185.55 KiB) Viewed 4086 times

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[Gillybob]

Thanks for that. In Roy Darlington's book he recommends using a Ross linkage on a gamma. In the images however, it is clearly symmetrical. This will mean that he can not have used his own sizing recommendations. Can you recommend any good books?
I expect that when I build my engine there will be teathing problems, but if I don't get the fundimental right from the start, I don't have a chance of building an effecient engine.

[Ian S C]

The Ross Yoke in a GAMA motor does not have to be asymmetric, you can make the displacer larger than the power cylinder as is done with a V type GAMA with a single crank on the crank shaft.
I took some new photos yesterday, but my computer doesn't want to know my camera, so it won't down load them. It's a Sony that I bought around Christmas 2005, I think I might need a new one.
Ian S C