Its been years since I did any complex transformation of formulae. Could someone help. Is there a way to simplify the following formulas , preferably to remove some of the square or square roots? They are transforms for my delta robot. For non programmers pow(x,2) is x squared sqrt(x) is the square root of x 0.866025 is my approximation of Sin 60 if that helps. T1 = sqrt(pow(F,2) - pow(sqrt(pow((J * -0.8660254) - (x - (V * 0.8660254)),2) + pow((J * -0.5) - (y + (V * -0.5)),2)),2)) + z; T2 = sqrt(pow(F,2) - pow(sqrt(pow((J * 0.8660254) - (x + (V * 0.8660254)),2) + pow((J * -0.5) - (y + (V * -0.5)),2)),2)) + z; T3 = sqrt(pow(F,2) - pow(sqrt(pow(0 - (x),2) + pow(J - (y + V),2)),2)) + z; I'm offering a pure maths degree from the University of Delta Robot for the first correct answer! https://reprap.org/forum/read.php?1,68467,68467#msg-68467 Fri, 11 Sep 2026 13:23:23 -0400 Phorum 5.2.23 https://reprap.org/forum/read.php?1,68467,68509#msg-68509 https://reprap.org/forum/read.php?1,68467,68509#msg-68509
If you want to take a look at the design go to the link below and also a video on youtube of it working. I'm just tidying up the firmware, hence the drive to simplify the equations.

Helium Frog Website

There is also an excel spreadsheet which performs the calculations

Excel document]]> martinprice2004 General Thu, 16 Dec 2010 07:16:20 -0500 https://reprap.org/forum/read.php?1,68467,68508#msg-68508 https://reprap.org/forum/read.php?1,68467,68508#msg-68508
I'll take a further look at it tomorrow and see if I can come up with anything.

BTW: One of the reasons for asking is that some combinations of sin/cos formulas can be transformed into other combinations, which might be easier for you to calculate.

Do you ever see that angle (60 in one, 30 in the other) changing?]]> Cefiar General Thu, 16 Dec 2010 06:14:37 -0500 https://reprap.org/forum/read.php?1,68467,68505#msg-68505 https://reprap.org/forum/read.php?1,68467,68505#msg-68505
I'm trying to do all the calculations in an arduino mega firmware, that way I can use off the shelf PC G Code software to drive the robot.

Is there any stuff on the net how to calculate the curve fits for these equations?]]> martinprice2004 General Thu, 16 Dec 2010 05:12:31 -0500 https://reprap.org/forum/read.php?1,68467,68501#msg-68501 https://reprap.org/forum/read.php?1,68467,68501#msg-68501 Greg Frost General Thu, 16 Dec 2010 04:04:02 -0500 https://reprap.org/forum/read.php?1,68467,68476#msg-68476 https://reprap.org/forum/read.php?1,68467,68476#msg-68476
eg: pow(sqrt( _____ pow((J * -0.8660254) - (x - (V * 0.8660254)),2) + pow((J * -0.5) - (y + (V * -0.5)),2) _____ ),2)

You should be able to eliminate that straight away.

PS: Closing bracket indicators in text editors are your friends here.

Q's:

Is that actually 0.5 in these formulas, or is it a pre-generated value of something say like sin(30) ??

Do you need to generate T1 thru T3 for the same set of values? There's quite a bit of commonality between them, so you could probably break them down into common parts and substitute here and there.]]> Cefiar General Wed, 15 Dec 2010 17:18:13 -0500 https://reprap.org/forum/read.php?1,68467,68467#msg-68467 https://reprap.org/forum/read.php?1,68467,68467#msg-68467
Is there a way to simplify the following formulas , preferably to remove some of the square or square roots?
They are transforms for my delta robot.

For non programmers
pow(x,2) is x squared
sqrt(x) is the square root of x
0.866025 is my approximation of Sin 60 if that helps.

T1 = sqrt(pow(F,2) - pow(sqrt(pow((J * -0.8660254) - (x - (V * 0.8660254)),2) + pow((J * -0.5) - (y + (V * -0.5)),2)),2)) + z;

T2 = sqrt(pow(F,2) - pow(sqrt(pow((J * 0.8660254) - (x + (V * 0.8660254)),2) + pow((J * -0.5) - (y + (V * -0.5)),2)),2)) + z;

T3 = sqrt(pow(F,2) - pow(sqrt(pow(0 - (x),2) + pow(J - (y + V),2)),2)) + z;


I'm offering a pure maths degree from the University of Delta Robot for the first correct answer!]]> martinprice2004 General Wed, 15 Dec 2010 14:19:14 -0500