Kinematics

[fer_mayrl]

For all you folks that dont follow the groups on yahoo, there has been an ongoing talk about parallel kinematics implemented within Mach, by using the formulas implemented by art on some of the latest versions of Mach.
Its and interesting concept. Now as they say, the sky is the limit! (not really)
I was just hoping if anyone can tell me if series kinemetics can be implemented in the same way, I have been trying to do to do the math, and it is not as simple as for the parallel kinematics i have been practicing on.
Best regards
Fernando

[fer_mayrl]

This is kind of what i figured i could do, the equations on top are the once i came up with, but i cant put the angles in terms of x and y the way they are supposed to be input in mach formulas.
I tried using software to solve for the angles, but all i get are weir answers with imaginary numbers, any ideas?
Regards
Fernando

[fer_mayrl]

Ok after some help from Graham S. we have come up with the equations for the system above, after some testing I have found the following:
1) the equations work at least for quadrants 1 and 4
2) The gear reduction needed on each arm is pretty large, about 100:1 according to my calculations, gearheads of that ratio cost upwards of 1,000 dlls.
3) The resolution is variable depending on the position of the arms, having a resolution of about 0.015" when both arms are horizontal, and a resolution of about 0.021" when both arms point in a 45º angle, when the tool is closest to the pivot point of the first arm, the resolution comes down almost to 0.002", all this considering a 4'x8' working envelope, and a 100:1 gear reduction.
4) With that kind of reduction, and using a 10x microstep on a 200 step per revolution stepper with mach 3 at 45KHz, the arms would turn at about 10 rpm, which again would make the max feedrate of the tooltip variable because of the distance from the tip to the centers of rotation.
5) Making a rigid enough member and joint for this configuration is no easy task.
6) The implementation of the kinematic formulas on mach 3 works on an end of move basis, they are not calculated on a step by step basis, this means that if you make a move from (5,6) to (5,-6) instead of getting a straight vertical line, you would actually get a semicircle starting and ending on those points. This makes the generation of the toolpath a bit difficult because you have to segment the toolpath in your CAD program in order to get acceptable results, this is not too troublesome in a 2 axis toolpath, but it its on a 3d contour.
7) manual jogging works the same way as in point 6)

There are a ton of issues as you can see that would make this machine not an easy task to build and operate, but it is still a feasible proyect, i would like to build one of

these, the only things stoping me from doing this is the following:

1) Formulas being calculated on an end point basis and not step by step.
2) Not being able to use a bigger reduction to get acceptable resolution and keeping feedrate acceptable (both for plasma use at least)

I guess number 2 would not be a problem if using a Grex.
Number 1 is a bit more trouble since a new calculating algorithm has to be coded into mach 3, although art has expressed interest in implementing this, I am sure its not a priority. So until that day comes, i will put this build on hold for now.
Best Regards
Fernando

[fer_mayrl]

Art or Brian,
could you tell me if "proper" implementation of kinematics will be added to mach?
I have just installed EMC to see if i can get kinematics to work, but its HARD!
I just need to know, if this will be implemented somewhere in the future, i will not loose my time with EMC.
Thanks
Fernando

[Brian Barker]

I think it will with the Grex... But that is some time out and it is also up to Art

[fer_mayrl]

Lets hope, its not too far out!
And I hope the G-rex is not needed, but if is, there would be a good excuse for me to get one.
THnks
Fernando

[benergybenergy]

Im having a bit of trouble with max and desired feed rates in formulas.
I use formulas extensively for muliaxis tool length compensation as well as cartesian to polar machine driving. Does anyone know the hierarchy of max feedrates when using formulas. if multiple variables are used will it slow other axis down to slowest actual outputted axis speed or use values pre formula. Im in a situation where i have max feedrate changes across a rage of rotary movements (elliptical rather than rotary motion)
benergy