The Stewart Platform (why the joints?)

[Trying2Learn]

TL;DR Summary

qualitative description of the platform

Good Morning

As I have understood, the standard Stewart platform has six legs.

Each leg consists of a lower and upper body, connected by a translational joint (TJ) (that enables extension and contraction)

The bottom body of a leg, connects to the base plate via a UNIVERSAL JOINT (UJ)
The top body of a leg, connects to the top plate via a BALL AND SOCKET (BSJ)

An actuator forces the extension of the translational joint...

The other two -- UJ and BSJ -- allow rotations.

Without going into the closed loop constraints, or any advanced kinematics, could someone explain to me, in works, why the UJ was chosen for the bottom and SJ for the top?

 

[Baluncore]

The UJ or BSJ can be used throughout. A BSJ is less able to handle tension.
A BSJ must be lubricated and sealed with elastic bellows, which can be difficult.
A UJ can have needle roller bearings, with a better and more efficient lip seal.
Contaminants can enter a BSJ if it opens upwards or is at the bottom of a structure.
The upper joints are clear of the ground and protected from above by the platform.

 

[sophiecentaur]

I can't remember hearing of a Sterwart platform by name, although I have (obviously) seen them on video, used for various applications. I found this link which is the coolest thing I have seen all day. Mr Stewart has brightened my day.

 

[phyzguy]

I've used these things quite a bit in astronomy for positioning, but we always call them "hexapods". I had never heard the Stewart platform name.

 

[Baluncore]

... , but we always call them "hexapods".

It is not really a hexapod because it does not walk on six legs like an insect.
Maybe it does have six legs, but it has only three feet, and it does not walk.
https://en.wikipedia.org/wiki/Hexapod_(robotics)

 

[phyzguy]

It is not really a hexapod because it does not walk on six legs like an insect.
Maybe it does have six legs, but it has only three feet, and it does not walk.
https://en.wikipedia.org/wiki/Hexapod_(robotics)

I'm not defending it. I'm just saying that everyone I work with calls these devices hexapods.

 

[Baluncore]

Without going into the closed loop constraints, or any advanced kinematics, could someone explain to me, in works, why the UJ was chosen for the bottom and SJ for the top?

Having scanned the book on the subject; Parallel Robots by J.P. Merlet - 2'nd Edn', I think I may have stumbled upon the foundational reason for the Cardan Joint - Ball Joint mix.

The linear actuator is placed in the leg, between the two end joints. The electric cables, or hydraulic hoses, that control the actuators can be bent, but should not be twisted, where they cross the lower joints at the base, hence the use of Cardan Joints to maintain axial control of the lower leg.

Some screw actuators need axial rotation control at both ends to prevent them creeping, but then the length of the screw would change slightly as other actuators were adjusted and the platform rotates, so the screw rotation needs to be controlled at the actuator nut, with a ball joint at the top to allow for one degree of rotational freedom in the leg.

I believe the original Gough platform of 1947 had UJ = Cardan joints at the bottom, with ball joints at the top. Stewart publicised the device 20 years later, hence another name, the Stewart-Gough Platform.

 

[Trying2Learn]

Having scanned the book on the subject; Parallel Robots by J.P. Merlet - 2'nd Edn', I think I may have stumbled upon the foundational reason for the Cardan Joint - Ball Joint mix.

The linear actuator is placed in the leg, between the two end joints. The electric cables, or hydraulic hoses, that control the actuators can be bent, but should not be twisted, where they cross the lower joints at the base, hence the use of Cardan Joints to maintain axial control of the lower leg.

Some screw actuators need axial rotation control at both ends to prevent them creeping, but then the length of the screw would change slightly as other actuators were adjusted and the platform rotates, so the screw rotation needs to be controlled at the actuator nut, with a ball joint at the top to allow for one degree of rotational freedom in the leg.

I believe the original Gough platform of 1947 had UJ = Cardan joints at the bottom, with ball joints at the top. Stewart publicised the device 20 years later, hence another name, the Stewart-Gough Platform.

Thank you, Baluncore, for your response. I will now take the time to look it up.

Before I do, however, since you did look, could I ask a few short questions?

1. Are these two types of joints, required for a solution to the closed loop kinematics?
2. Or would two UJ joint work (one at the top and one at the bottom)?
3. Are UJ and SJ required for a closed loop kinematic analysis, or just for greater control?

 

[Baluncore]

Before I do, however, since you did look, could I ask a few short questions?

1. Are these two types of joints, required for a solution to the closed loop kinematics?
2. Or would two UJ joint work (one at the top and one at the bottom)?
3. 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.

 

[Trying2Learn]

thank you, everyone!