Trying2Learn said:
Before I do, however, since you did look, could I ask a few short questions?
- Are these two types of joints, required for a solution to the closed loop kinematics?
- Or would two UJ joint work (one at the top and one at the bottom)?
- Are UJ and SJ required for a closed loop kinematic analysis, or just for greater control?
Unfortunately there can be no general answer.
You must first select your linear actuator and power source;
You will then probably place a non-rotating joint at the base;
followed maybe by a ball joint at the top of each leg.
The joint type selection is not explicitly specified in the two paragraphs on joints in the book, (pages 29 & 30). There is more concern that pairs of leg-ends cannot actually meet at ideal coincident points.
Joints are an irrelevancy to the spatial programmer of the platform. The selection of the joints and the placement of hoses and cables is left as a challenge for the engineer. You must look at the pictures and wonder how the hydraulic hoses or cables would handle the situation. Conduits, cable trays, or high pressure hydraulic hoses need to follow 'U' or 'S' shaped paths in a single plane, with wide radii of curvature. No axial twist is possible without kinking or the hose end couplings undoing. As I see it there may need to be a bulkhead connector with a right angle elbow attached to the crux of the Cardan joint, to guide and control each passing hose or cable. Maybe there is a simpler solution.
Since the platform can rotate relative to the base it is essential that there be an axial degree of freedom in each leg. If you used Cardan UJ at all points, then there would need to be an extra freedom provided to avoid twisting the leg, which would be like a torque-tube, or the drive-shaft on a car. That appears to promote the use of one ball joint at the top of each leg.
Consider a hydraulic cylinder actuator leg. The rod and piston can rotate in the cylinder but that would cause wear and be inefficient when pressure was applied to the seals. The piston and rod seals rest in grooves, they are not positively prevented from rotating in the groove. The piston and rod seal lips self-lubricate in normal use, but not in rotation. I have seen pistons that have unscrewed from the internal end of the rod. Without a ball joint, that is a real possibility.
Consider a ball screw or an acme threaded actuator leg. The axial rotation can be handled by the ball screw but there would be a length variation over half a pitch. That would be either very interesting, or difficult to compute. An acme thread and nut would wear if there was no ball joint to swivel. Hysteresis in the linear screw actuator requires that the rotational position of the nut and screw be tightly controlled.
Maybe instead of a ball joint you could specify a ball-race swivel at the top of each leg, below an upper UJ.
Since front wheel drive cars have become more popular, replacement constant velocity joints have reduced greatly in price. CVJs have low friction with internal rolling balls. That might now make a good joint if the axial play could be minimised.
Ball joints tend to be more rigid when the ball supporting shaft is at right angles to the leg. Look at the ends of 'gas struts'.
If you can constrain the design in size, force and actuator type, then a minimum solution can be proposed and evaluated. At the moment there are to many interacting possibilities.
