Best if the drawings mentioned are in another open window. These have been done in Generic CAD and captured as bmp. The geometry underlying the pixels is precise and explicit. 

Method.bmp shows in general how the action of these supensions is laid out. The bmp shows ovals but the actual geometry was circular in the CAD. The two circles are based on the length of the main links. Yellow is upper and green lower. Brick is the upright. First, the end positions are chosen for lower link, and circle (not shown) is drawn about the end, of radius equal to the distance between outer suspension pivots. Where that circle intersects the upper circle then is the corresponding postion of the upper link. Other FFE positions are done in the same way; only four are shown here. The above process is easily automated. The entire circle is not needed for actual FFE layout. The experimenter would choose a section of the design for farther investigation. For example the upper two positions of this one have low SI angle change for a given amount of travel. Usually a portion of the curve is easily chosen with desired characteristics no matter what proportions of the linkages. 

The ffe.bmp is a general layout of the unequal length quadralateral FFE. Three positions of the linkage are shown in heavy solid lines, blue being most extended, red being approx midway and yellow being fully compressed. Pivots at frame are to left and steering axis is to right; the wheel is off to the lower right on steering axis extended. Shown in dash are extensions of linkage to the three ICs, only blue IC being in the pic. This is not a good suspension because of great overall SI angle change, but it's OK illustratively. According to IC method, in dash/dot are the corresponding lines of drag links to the ICs from upright, for four attachment points. The same color has been used for each attachment point in each position of the FFE. The intersections of these sets of dash/dot lines near the frame end of the FFE (inside green oval) are said to be the desired location(s) of rear drag pivot.

ffe1.bmp is a detail of the area about the lower link and frame pivot, showing the intersections of the drag link lines by color, IE by attachment and position. In no three FFE positions do these sets of lines intersect at a common point, therefore no one intersection serves all positions. Presumably by the IC method the distance to the upright from intersection is the drag link length, but in the CAD geometry it's possible to tell that no two lines from any given intersection, corresponding to only two positions, will have the same length to upright.

The error.bmp shows the same view but only the intersecting parts of the drag lines. The drag length error and bump steer for each attachment point on upright is related to the size of these triangular figures. Notice that the error reverses sign outside vs inside, by the triangles pointing opposite directions. The error triangles grow larger with attachment points around the midpoint of the linkages, then smaller again toward the other link. They increase in size rapidly outside the main linkage.

These error triangles are an artifact of a larger phenom, showm partly in error1.bmp; this shows in white dragline intersections of serial FFE positions in method.bmp, for one attachment point only. The curve formed by drag line intersections of all FFE positions would be closed and with two inflection points; depending on properties of the FFE itself that can range from banana to almost round heart shaped, the same overall shape as the axle trajectory itself. In error2.bmp, with linkage line widths reduced for clarity, it is seen that curves passing thru corresponding intersection points cross each other at the lower pivot, IE drag length error when link is coaxial is equal to zero, and so is bump steer. In the geometry, this is nothing more than a dot/dash line overlying the dash line in ffe.bmp and moving perfectly in accord with it. 

Suspension induced bump steer is worst overall with drag attachment outside links and second worst about halfway between them. It can be arbitrarily reduced in magnitude by only limiting linkage angulation in suspension or steering. Whereas the IC method is in general insufficient to produce drag link locations, it does serve to prove the special case of coaxliality.  Suspension induced bump steer in FFE is entirely eliminated by placing drag coaxial with either main link.

Some bump steer will still reside in FFE that are non-parallelogram, as result of steering interacting with suspension travel thru changes in SI angle. The crux of this is that if angle between idler axis and steering axis changes from zero, the locus of the ends of the drag links cannot be the same or project the same into a given plane. Careful selection of FFE layout minimizes this by controlling overall SI angle change. Choosing the portion of the overall curve having one inflection point approx at the middle of travel means SI angle change is almost equally distributed about that point, and minimal. This is done in practice by having the steering head and idler axis parallel at that point in the travel. The bmp discussed below show how the bump steer is quantified, using that point of parallel S and I axes as basis and a typical SI angle change for comparison.

The steer.bmp shows four schematics associated with parallelogram and one with non-parallel FFE. The two on left are top and side view of paralleogram linkage showing steer and travel, with coaxial drag link. It's as good there as any place in paralleogram by definition and illustrates the concept of coaxiality in general. The upper right two drawings are top and side of the steering components at points deflected 22.5 and 45 deg and at the upper travel position. The yellow is midline of the main lower link (in midplane of bike). Green is the drag link at 45 and maroon is at 22.5 deg. Yellow dash arcs are travel of the lower front suspension pivot. Dark blue in top views is the idler arm and steering radius of the upright, and the arcs the ends of drag travel thru. The rightmost upper arc has some white segments, actually segments of an ellipse projected into it, to be discussed later; it's necessary to make precise determination of the actual bump steer. The small green and maroon crosses are the ball joints in the drag link, in two positions. A maroon steering radius is there also, masked under light blue. The steering and idler axes are the vertical brick lines. There is no top link shown because we are defining our SI angle as 0 deg or in the last example 2 deg, and that about the bottom link. The white and light blue vertical lines are projections from the last example and will be discussed later. In these first four the projections of the locus of the ball joints in ver plane and hor plane are the same at each end at all times, producing no bump steer. In fact, they're the same projected into any plane. 

The last example differs from immediately above only by having the steering axis inclined 2 deg to left. In this case, the ball joints cannot describe the same projected locus because the steering plane is 2 deg different from the idler plane. This is shown at greater zoom in steer1.bmp, with the green and maroon drag link ends are left in same plane as in sketch just above. The dark blue line is the new plane of the steering, perpendicular to the stem and tilted the same 2 deg. The drag links no longer reach the same point in this plane but the connection does have to lie on arcs, white, using the drag link as radius. These intersect the steering plane slightly more to the left and that point is projected upward by the white and light blue lines above. 

The steer2.bmp shows a portion of a previous example with the light blue and white lines projected onto it from below, and now you can see the geometry unmasked. The right-most each of the two radial line pairs is the position of the steering radius at 22.5 (maroon) and 45 (blue) degrees deflection in parallegram case. These intersect the blue portions of arc, the parallel case locus. The leftmost of the two pairs each, (white and light blue) is the steering radius intersecting the ellipse, the 2 deg tilted locus of this particular non-parallel case. It is only by projecting these two loci into same plane that we can measure the effect of SI angle on bump steer. The angles between lines of each pair then represent the amount of bump steer in this FFE at the illustrated travel and deflection from base. Here it's about 1.1 deg bump steer at 45 and .5 deg bump steer at 22.5 deg steering and full travel. 


Drawing and text files are all (C) OH McKagen, Sept 1, 2000. All rights reserved and no reproduction is allowed by any means.