Figure 2 displays a more general form of the Ross linkage
with the aim to produce
motions of points 4 and 4' which have less lateral movement. In this figure
the points 1, 3, 5, and 5' lie on a dashed straight line. Lines
4'-5' (=length e') and 4-5 (length e)
are both perpendicular to this line.
The distance between points 3 and 5 is called if, which assumes negative
values if point 5 lies between points 1 and 3. The same holds true for
the points 3 and 5' whose distance is f '.
The distance between points 1 and 3 is called d.
This setup reduces to the
classical (sometimes called symmetric) Ross linkage if f=f '=0 and
e=e'.
Putting aside for the moment the option of connecting a piston to point 4', we concentrate on the motion of point 4 which is facilitated by the rocking lever 2-3, the crank 0-1, plus only the right side of the triangular plate described by the points 1-3-4. This reduced drive is now essentially what is known in the kinematics community as a 4-bar linkage and it is helpful to analyze that part first and get a first feeling on how varied the orbit of point 4 might be. These orbits can take on the shape of a simple oval all the way up to a double-eight figure. Program 4bar : Analysis of 4-bar linkage including some optimization plus links to images of various orbits of point 4
One hint though before you dive into using this program.
It is fairly easy to specify values for the parameters (1) c < √ a² + b² - ( r - d ) (2) c > √ a² + b² + ( r - d ) (3) d > r Condition (3) is a consequence of (1) and (2)Starting program RossInto the dialog box below you must enter the nine parameters
r a b c d e f e' f '. In response program Ross will give a lot
of information about the curves the two connecting point, 4 and 4', produce
as the crank turns 360 degrees. An animation is provided as well. To produce a useful geometry for your Ross linkage you can of course follow your own ideas or follow one of the following two options : Option 1 : You start with a geometry Andy Ross³ first used. f = f ' = 0 ; e' = e = b = d = half of desired horizontal distance between point 4 and 4'a = c > bChoose r to achieve desired strokeOption 2: Use the optimization feature of program Program 4bar to provide you with values for the first seven parameters, r a b c d e f, with very limited input. Connecting point 4 will move almost exactly on a vertical straight line (you specify the maximum lateral motion) and will have the specified stroke. Program 4bar will not provide any information about the length e' but choosing f ' will result in a stroke for point 4' approximately equal to that of point 4 and you can adjust accordingly. The optimizing mode of program 4bar needs as input only the ratios a/r and e/r and determines the remaining parameters. For either option the choice for the parameters e' and f ' is yours. You might want to start with e'=e and f '=0. This program then will suggest to you a better value for f ', but uses the value you have specified. In general, an increase of e' with optimal f ' will increase the stroke and quality of point 4' and shifts the phase lag between points 4 and 4' to higher values. Please observe the order in which the nine parameters have to be provided. References¹Urieli I and Berchovitz D M , Stirling Engine Cycle and Analysis, Adam Higler, Bristol, 1984² Organ Allan J. , Thermodynamics and Gas Dynamics of the Stirling Cycle Machine, Cambridge, 1992 ³ Andy Ross, Making Stirling Engines, 1993 |