For tonight: How to eliminate bump steer, and why I don't want to do that.
So most people have heard of bump steer and how bad it is. In a sense this is true, bump steer can make a vehicle frighteningly unpredictable to drive. Hitting a bump in the road can cause the vehicle to spear off into the nearest hedge often toward small children and/or puppies. There are some absolute garbage suspension "upgrade" parts out there and it makes my head hurt every time I see a car with them installed. Let's look at the old suspension design. For the purposes of this point assume all drawings are of the front steer variety where the steering arm is in front of the steering axis.
I've added a red line to represent the tie rod. The spindles on those old cars were short, the wheels small, and the steering slow. So the tie rod had to be mounted about the lower ball joint in order to not run into the wheels. Conversely the engines sat low in the chassis to allow a lower hood line, so the inner tie rod had to be low enough to allow the tie rods to pass under the oil pans when the steering was turned.
With everything simplified down you can see the lower control arm and tie rod make an X viewed from the front. As the suspension compresses the bottom of the spindle moves away from the frame, but the steering arm of the spindle moves toward the frame. This means the tire is turning towards the frame when the suspension compresses, bump steer. Where things really get scary is if your tie rods are different lengths the rate at which this turn happens is different from side to side. If you're driving down the road and even if you hit something the exact same height with the front tires at exactly the same time, you could have one wheel turn in 2 degrees while the other turns in 7 degrees. A lot of the rack and pinion conversions I've seen on old cars position the rack off center making the tie rods different lengths.
Adding a tie rod to our line drawing of better control arm alignment can see better positioning of the tie rod.
The lines obviously don't cross there, so as the suspension compresses the lower ball joint and steering arm move towards the chassis at a matched rate. The lengths of the lower control arm and tie rod need to be matched too, the idea being the lateral movements of those attachment points match as the lines move in an arc around their inner attachment points. Also the two tie rods need to be matched as closely as possible in length, but it isn't as tire wearing a bad toe alignment so tie rod length takes a back seat to toe alignment.
An interesting way to look at it is that if you extend the upper and lower control arms along an imaginary line through space where those lines meet is also where a third line of the tie rod meets. I didn't do a drawing of the awful suspension like this, but it's obvious it doesn't work with that since the two lower lines cross without the imaginary extensions. So that's how to completely eliminate bump steer.
The funny thing about bump steer though, is it's considered advantageous to handling when a controlled version is designed into the suspension. That's really all passive rear steer is, and it's touted as the main advantage of 5 link or multi link rear suspensions. You can toe the tires out under braking to aid rear stability and toe them in under acceleration to make the car feel more nimble. This can work a little on the front end as well, tire scrub radius is more interesting though.
When you turn the car the front wheels turn, but the inside tire is making a smaller circle than the outside tire. That's why differentials exist, the outside tire goes farther than the inside and if they were locked together the tire would have to slip to make the turn. It does this even with the wheels not linked at all too though, the inside tire is a smaller circle to that tire needs to be turned more than the outside tire. If the tires turn the exact same amount there has to be tire slippage in order for the vehicle to actually turn.
One of the fun ideas behind that then, is that if you turn right you load the left tire compressing the suspension. The left tire wants to be turned less than the right tire, you can use bump steer to make this happen. The lower ball joint moves in as the suspension compresses hopefully, so you want the steering arm to move in just a smidge more. That imaginary line trio needs to get separated so there isn't a single point of intersection, the lower control arm and tie rod should cross slightly outboard of the point the upper and lower arms cross. Less scrub when turning means you have more of the available friction of the tire able to be used for actually turning the vehicle. That's why I don't want zero bump steer.