Compensating Robot Arm Deflection for End Weight

[barry_scott]

Hi guys, I'm doing a robotics project that requires me to compensate for the bending of the arm due to an end weight. I can calculate the deflection at the end of the arm for a given weight e.g.

End link horizontal (90 degrees), end weight = 1000g, deflection = 10mm
From this i can calculate the angle down to the deflected end point eg 3 degrees. Now the problem comes when i try to compensate for this deflection to get the end point to where i actually need it to be. Simply aiming the arm 3 degrees higher won't work as changing the beam angle changes the amount of deflection at it's end!

So basically given a target angle, say 90 degrees i need to know what actual angle to put the beam at so that when the deflection is applied the end point is at 90 degrees. But this requires me to know the beam angle to calculate the deflection to find the beam angle?

This is confusing me greatly and any mathematical insights would be greatly appreciated!

 

[fresh_42]

You need to express the deflection function $D(F,\varphi)$ with a weight force $F$ at an angle $\varphi$, which in your example was $\varphi=90°$ as a function of $D(F_v,\varphi$ instead, where only the vertical component $F_v$ of $F$ plays a role, since it is all which causes the deflection. $F_v$ is dependent on $\varphi$. In the end you can solve for $D(F_v,\varphi)=0$.