I've done this before, but it was with equations. Realizing pictures might be more effective, I submit the following:
In Fig. 1, I've drawn a vertical line with arbitrary length. We'll consider this to be a "body" upon which forces can be exerted. At the bottom of the line, I've drawn a horizontal line, again with arbitrary length. This line (arrow) is a force vector. That is, its length is proportional to the magnitude of the force and its direction indicates the force direction. I've also added some "links." One is attached at the top of the vertical link and the other is attached at some arbitrary point on the vertical line. The links are angled (again, arbitrarily), so, if link lines are drawn, they intersect at what we call the "instant center" or "IC."
In Fig. 2, I've replaced the links with force vectors. When we're working with the forces and moments (torques) acting on a body, everything must be "balanced." That is, there must not be an "extra" force or moment which would send the body spinning and/or moving into space. We're not to this point in the diagram, but we're getting there. Those angled forces have both horizontal and vertical components. The difference between the horizontal components must be equal and opposite to the original force at the bottom of the body.
So, the horizontal component of the force attached at B, less the horizontal component of the force attached at C, must be equal in magnitude...but opposite in direction...to the force AK.
In addition, there must be a moment balance. So, taking moments around A, the distance AB times the horizontal component of the force at B must be equal in magnitude, but opposite in direction, to the distance AC times the horizontal component of the force at C.
With these two bits of information, we can determine the force vectors acting at B and C, as also shown in Fig. 2.
To maintain a force balance, the force acting at A must have a vertical component. I could simply say that this is equal in magnitude, but opposite in direction, to the sum of the vertical components acting at B and C, but, to make this clearer, I've added the equal and opposite force vectors in Fig. 3. AT is equal and opposite to HB, TL is equal and opposite to CD, LP is equal and opposite to GH, and PS is equal and opposite to DF. The resultant, as you can see, goes directly to the IC.
Since we have seen this to be true for a completely arbitrary case, it is safe to assume that, for the "real life" case of an axle assembly (Fig. 4), the resultant force at the tire patch (the sum of forward thrust and weight transfer), must also point to the IC. I have labelled this force action line the "no squat/no rise line." This implies that the tangent (slope) of this line also happens to equal the center of gravity height divided by the wheelbase. An IC on this line would further imply, then, that the car would neither squat nor rise on launch. Since a line is comprised of an infinite number of points, it follows that it also contains an infinite number of possible ICs which would yield the same launch performance. The car, in other words, "knows" that a force is acting on it along a certain line, but is unable to determine where, on that line, it is acting. So, rather than define a specific "up" and "out" for an IC, it is far more reasonable to define the slope of the force action line upon which the IC is located. If the slope is greater than the ratio of center of gravity height to wheelbase, the car will rise; if less, it will squat. If we divide a given slope by the neutral slope and then multiply by 100, we have that which is called "percent antisquat."
Since parallel lines intersect at infinity, another 4link design would be one in which the links are parallel to each other and parallel to the desired force action line. Adjustment would be a matter of positioning vertically an end bracket.
As for my reason for posting, I'm trying to make it easier for dragracers to communicate. The use of "ups" and "outs" has caused a great deal of confusion. One racer will recommend one set and another racer recommends a "different" set. But, if they're on the same constant percentage antisquat line, they're NOT different! They're the same, as anyone with CAD software can prove for himself.
Personally, I would find it much easier to use a bubble angle tool and measure the angle of a parallel link setup than to input my link end measurements into software. Art Morrison, for one, offers a parallel link setup, but, as far as I know, it lacks adjustability. If Mr. Morrison...or anyone...would offer an adjustable parallel 4link that could handle high horsepower engines, I'm certain he would find a large number of racers who would gladly opt for the "loosen, tap with a hammer, check with the bubble, and tighten" method of 4link adjustment.
In Fig. 1, I've drawn a vertical line with arbitrary length. We'll consider this to be a "body" upon which forces can be exerted. At the bottom of the line, I've drawn a horizontal line, again with arbitrary length. This line (arrow) is a force vector. That is, its length is proportional to the magnitude of the force and its direction indicates the force direction. I've also added some "links." One is attached at the top of the vertical link and the other is attached at some arbitrary point on the vertical line. The links are angled (again, arbitrarily), so, if link lines are drawn, they intersect at what we call the "instant center" or "IC."
In Fig. 2, I've replaced the links with force vectors. When we're working with the forces and moments (torques) acting on a body, everything must be "balanced." That is, there must not be an "extra" force or moment which would send the body spinning and/or moving into space. We're not to this point in the diagram, but we're getting there. Those angled forces have both horizontal and vertical components. The difference between the horizontal components must be equal and opposite to the original force at the bottom of the body.
So, the horizontal component of the force attached at B, less the horizontal component of the force attached at C, must be equal in magnitude...but opposite in direction...to the force AK.
In addition, there must be a moment balance. So, taking moments around A, the distance AB times the horizontal component of the force at B must be equal in magnitude, but opposite in direction, to the distance AC times the horizontal component of the force at C.
With these two bits of information, we can determine the force vectors acting at B and C, as also shown in Fig. 2.
To maintain a force balance, the force acting at A must have a vertical component. I could simply say that this is equal in magnitude, but opposite in direction, to the sum of the vertical components acting at B and C, but, to make this clearer, I've added the equal and opposite force vectors in Fig. 3. AT is equal and opposite to HB, TL is equal and opposite to CD, LP is equal and opposite to GH, and PS is equal and opposite to DF. The resultant, as you can see, goes directly to the IC.
Since we have seen this to be true for a completely arbitrary case, it is safe to assume that, for the "real life" case of an axle assembly (Fig. 4), the resultant force at the tire patch (the sum of forward thrust and weight transfer), must also point to the IC. I have labelled this force action line the "no squat/no rise line." This implies that the tangent (slope) of this line also happens to equal the center of gravity height divided by the wheelbase. An IC on this line would further imply, then, that the car would neither squat nor rise on launch. Since a line is comprised of an infinite number of points, it follows that it also contains an infinite number of possible ICs which would yield the same launch performance. The car, in other words, "knows" that a force is acting on it along a certain line, but is unable to determine where, on that line, it is acting. So, rather than define a specific "up" and "out" for an IC, it is far more reasonable to define the slope of the force action line upon which the IC is located. If the slope is greater than the ratio of center of gravity height to wheelbase, the car will rise; if less, it will squat. If we divide a given slope by the neutral slope and then multiply by 100, we have that which is called "percent antisquat."
Since parallel lines intersect at infinity, another 4link design would be one in which the links are parallel to each other and parallel to the desired force action line. Adjustment would be a matter of positioning vertically an end bracket.
As for my reason for posting, I'm trying to make it easier for dragracers to communicate. The use of "ups" and "outs" has caused a great deal of confusion. One racer will recommend one set and another racer recommends a "different" set. But, if they're on the same constant percentage antisquat line, they're NOT different! They're the same, as anyone with CAD software can prove for himself.
Personally, I would find it much easier to use a bubble angle tool and measure the angle of a parallel link setup than to input my link end measurements into software. Art Morrison, for one, offers a parallel link setup, but, as far as I know, it lacks adjustability. If Mr. Morrison...or anyone...would offer an adjustable parallel 4link that could handle high horsepower engines, I'm certain he would find a large number of racers who would gladly opt for the "loosen, tap with a hammer, check with the bubble, and tighten" method of 4link adjustment.