5 axis toolpath calculation

I have tried some of the tools people have so graciously shared such as Camel http://www.grasshopper3d.com/forum/topics/camel-grasshopper-output-...

and Lobster http://www.grasshopper3d.com/group/lobster but I couldn't get them to generate the proper code for my machine. I tired a different solution than using IK. I am taking the normals along the surface I wish to cnc and I am using surface CP to move them onto a sphere and then I am simply using the remap feature to convert the UV values to my B and C rotations. This seems to work well for 5 axis machines since you only need XYZBC. This definition allows you to input a surface and it will generate the cutting paths as one continuous curve without any retracts. This is a pretty limiting method but it's fun and fast to use if you are planning on machining a form that lends itself to this sort of operation.

b_c_angles_forsingualr_path_use.gh

5axis_surface_input.3dm

Here is a example of the curve it will create on the input surface.

Here is a video of the file being cut

Replies to This Discussion

Permalink Reply by Yves Gauvreau on May 15, 2013 at 4:46am

Hi,

You seem to have used a pretty clever way to evaluate the B and C angle. I'm very new to GH and if not to much to ask, I'd like you to explain in as much details as possible the method used to eval the angle.

I tried to figure it out by myself but unfortunatly the GH help on most component is pretty succinct to say the least.

Thanks for sharing,

Yves

Permalink Reply by machinehistories on May 15, 2013 at 12:31pm

I use the evaluate surface component to generate normal planes at the locations I wish to machine. I make a sphere with a size of 1 unit. I move all of these planes from the current location to the sphere center which in this case is also the origin. I then use surface closest point to place the oriented points onto the sphere. I then evaluate all of those points to get the UV coordinates on the sphere and I remap the u values from 0 to 1 : the rotation limits and then I remap the V from 0 to 1 : 0 to 360. It is kind of a strange approach but it works well. To me the math is little easier to think through rather than trying to solve for angles. I made an angle based solution in the past but it was hard to solve for positive and negative angles. With the current approach you can do that a bit easier based on your remap values and that way you can specify angle limits in relation to the machine you are using.

Permalink Reply by Yves Gauvreau on May 16, 2013 at 2:55am

I can understand this technique works fine for an XYZBC machine where the part is fixed but for other configuration like say an XYZAC where A is a trunnion table and C is a rotating table in the middle of A I don't see how this can work because the XYZ coordinate of the control point or bit tip is moved each time a rotary axis move. This is why I wanted to have a better understanding of your approach.

If I may again, if I understand correctly you use a Plane origin component to move each normal plane generated by the eval surface component using the F output (though I guessed it was a normal plane there is no mention of this in the help file I've seen) then you feed the moved normal plane to a Point oriented compoment. I can see you set the U and V to 0 and W input to 1. I can only guess at what this compoment those, I assume W is set to 1 to match you sphere radius and I assume this component kind of project the points on the sphere. You then use this point (points actually) to find its UVs values on the sphere. Since the sphere as a radius of 1 I can understand that these UV are related to the sin and cos of a vector or line from the center of the sphere to that point (maybe I'm wrong here) but I don't see the linear relationship implied by the use of the remap component with angles. Maybe you can explain this part a little more if possible.

Thanks,

Yves

Permalink Reply by machinehistories on May 16, 2013 at 11:51am

I am using an XYZBC machine so you might be right about it not working for other axis configurations although I think it could be adjusted to accommodate those machines. In terms of the linear relationship to the remap:

the current sphere is parameterized at 0 to 1 so the remap takes the current UV coordinate position and just scales it within the rotation values with U representing one axis and V the other. Here is an image that gives an example of a C axis rotation based on remapping a point value to a rotation value.