It's an over-constrained mechanism. The best simplification is to look at the instantaneous centers for the motion of two of the three tracks, and then calculate the orientation and speed of the third track to match.
Otherwise you have to figure out if one of the three will not be able to maintain static friction conditions and will slip and then see if there is enough power and traction remaining to the other two to overcome the slipping one. In some cases this will be an unstable arrangement - for example if two tracks are adjacent but are set to converge then the tracks may oscillate as the controlling friction shifts from one side to the other. Or if the tracks are parallel and adjacent ones are set to go forward and the center/forward track is set to go backwards, it may be that the front track slips or one of the adjacent ones does.
This complex behavior will change if the center of gravity shifts, applying more or less normal force.
AapMechE:
I think you’ve kinda asked your question the wrong way. If the link that 3DDave provided is a reasonable example of the machine (the tracks and slip form) you are talking about, then think about and try the following.... The controlling shape and radius’ will be those defining the back of the curb, and the three tracks are synchronized to provide this at the slip form. In today’s world, your machine control system (computer and software) does all the math and controls/drives all of the various components to achieve this. Actually, the machine operator is following a string or some such for elevation and curb location in plan and his controller stick actions cause the machine to follow this string. All of the functions of the machine are driven hydraulically and individually, so hydraulic flow rate, pressure, proportional valves, etc. etc. provide the correct motions, speeds and directions of motion.
For starters, for this exercise, assume a nice generous radius for the curb; then lay out the slip form system at that radius, to some scale. You know the x,y&z locations of the various components on your machine, convert them to cylindrical coordinates, and lay out the pivot centers of the three tracks w.r.t. the slip form center radial line. That is, a radial length from the center of curvature and an angle fore and aft of the slip form center line. This gives you the trig./geometric layout you need to work this problem out. It’s one big kinematics problem which the machine control system usually works out for the operator (or you). At any instant of time or travel the three tracks might be at different radii from the center of curvature and at different angles w.r.t. the slip form center line, so their rates of forward travel and their angles of attack might all be slightly different, to keep the machine properly oriented and traveling to follow the string. And, they may be changing as the radius of the back of the curb changes.
Correct dhengr... I am at the forefront of a redesign and am not using slew gears to have 360 degrees of turning at each track. I just want to make sure my stance is narrow enough with plenty of turn angle at each track (cylinder stroke) to guarantee the machine can match whatever software or string line is guiding my machine. You just stated a general overview of the obvious. 3DDave's statement was short and to the point and all I needed for directing my kinematics.
