COW arm - Revision history

Alnwlsn: /* The Real Math */

2019-08-22T15:04:58Z

The Real Math

@@ Line 72: / Line 72: @@
 Well, the math we just did above assumes all the pins, bearings, etc are along the centerlines of the two arm segments. In the arm we just built, this is not the case, as we used brackets that bring these pins away from the centerlines.  This means that the end of the arm we calculate for and the real arm are two different things. However, they are both rigid bodies, so in theory we should be able to add angle and/or distance offsets and correct for these off-axis hinges. To do this, I'm going to go back to GeoGebra and make a model accurate to the real arm, then pick the adjusted (projected?) measurements off to use in my kinematics.
 ==Files==
 * GeoGebra files for the ideal arm: [[File:Cow-arm-lower-upper-v3-ggb.zip]]
 * GeoGebra files for the real arm: [[File:cow-v6-arm-full.zip]]

Alnwlsn: /* The Real Math */

2019-08-22T14:55:28Z

The Real Math

← Older revision		Revision as of 10:55, 22 August 2019
Line 68:		Line 68:

	===The Real Math===		===The Real Math===
	[[File:Cow-real-arm-geogebra-v1.png\|thumb]]		[[File:Cow-real-arm-geogebra-v1.png\|thumb\|The geometry of the real arm looks much more complicated. The ideal arm is still there (the green lines), but I have added all the off-axis mounts and hinges that form the real arm.]]
	Once I got the above equations all into Arduino code and attached up the actuators back on the arm, I attached a pen to the end of the arm and tried to draw a square, going in straight lines. It came out lopsided, and lines that were supposed to be straight were curved. Why?		Once I got the above equations all into Arduino code and attached up the actuators back on the arm, I attached a pen to the end of the arm and tried to draw a square, going in straight lines. It came out lopsided, and lines that were supposed to be straight were curved. Why?

Alnwlsn: /* The Real Math */

2019-08-22T14:55:05Z

The Real Math

← Older revision		Revision as of 10:55, 22 August 2019
Line 68:		Line 68:

	===The Real Math===		===The Real Math===
			[[File:Cow-real-arm-geogebra-v1.png\|thumb]]
	Once I got the above equations all into Arduino code and attached up the actuators back on the arm, I attached a pen to the end of the arm and tried to draw a square, going in straight lines. It came out lopsided, and lines that were supposed to be straight were curved. Why?		Once I got the above equations all into Arduino code and attached up the actuators back on the arm, I attached a pen to the end of the arm and tried to draw a square, going in straight lines. It came out lopsided, and lines that were supposed to be straight were curved. Why?

Alnwlsn: /* Files */

2019-08-22T14:49:59Z

Files

← Older revision		Revision as of 10:49, 22 August 2019
Line 73:		Line 73:

	==Files==		==Files==
	GeoGebra files for the ideal arm: [[File:Cow-arm-lower-upper-v3-ggb.zip]]		* GeoGebra files for the ideal arm: [[File:Cow-arm-lower-upper-v3-ggb.zip]]
	GeoGebra files for the real arm: [[File:cow-v6-arm-full.zip]]		* GeoGebra files for the real arm: [[File:cow-v6-arm-full.zip]]

Alnwlsn at 14:49, 22 August 2019

2019-08-22T14:49:38Z

← Older revision		Revision as of 10:49, 22 August 2019
Line 11:		Line 11:

	At present, the arm design looks more like a crane or backhoe than an arm.		At present, the arm design looks more like a crane or backhoe than an arm.
	~~GeoGebra files for this design: [[File:Cow-arm-lower-upper-v3-ggb.zip]]~~

	==Encoders==		==Encoders==
Line 72:		Line 71:

	Well, the math we just did above assumes all the pins, bearings, etc are along the centerlines of the two arm segments. In the arm we just built, this is not the case, as we used brackets that bring these pins away from the centerlines. This means that the end of the arm we calculate for and the real arm are two different things. However, they are both rigid bodies, so in theory we should be able to add angle and/or distance offsets and correct for these off-axis hinges. To do this, I'm going to go back to GeoGebra and make a model accurate to the real arm, then pick the adjusted (projected?) measurements off to use in my kinematics.		Well, the math we just did above assumes all the pins, bearings, etc are along the centerlines of the two arm segments. In the arm we just built, this is not the case, as we used brackets that bring these pins away from the centerlines. This means that the end of the arm we calculate for and the real arm are two different things. However, they are both rigid bodies, so in theory we should be able to add angle and/or distance offsets and correct for these off-axis hinges. To do this, I'm going to go back to GeoGebra and make a model accurate to the real arm, then pick the adjusted (projected?) measurements off to use in my kinematics.

			==Files==
			GeoGebra files for the ideal arm: [[File:Cow-arm-lower-upper-v3-ggb.zip]]
			GeoGebra files for the real arm: [[File:cow-v6-arm-full.zip]]

Alnwlsn: /* Software/The Math */

2019-08-20T04:30:49Z

Software/The Math

← Older revision		Revision as of 00:30, 20 August 2019
Line 67:		Line 67:

	''20190819 - The above formulas have been fixed. In my original version, I mixed up which arm was link 1 and link 2, but it still seemed to work. Now that I want to use links of different lengths, I've had to fix it.''		''20190819 - The above formulas have been fixed. In my original version, I mixed up which arm was link 1 and link 2, but it still seemed to work. Now that I want to use links of different lengths, I've had to fix it.''

			===The Real Math===
			Once I got the above equations all into Arduino code and attached up the actuators back on the arm, I attached a pen to the end of the arm and tried to draw a square, going in straight lines. It came out lopsided, and lines that were supposed to be straight were curved. Why?

			Well, the math we just did above assumes all the pins, bearings, etc are along the centerlines of the two arm segments. In the arm we just built, this is not the case, as we used brackets that bring these pins away from the centerlines. This means that the end of the arm we calculate for and the real arm are two different things. However, they are both rigid bodies, so in theory we should be able to add angle and/or distance offsets and correct for these off-axis hinges. To do this, I'm going to go back to GeoGebra and make a model accurate to the real arm, then pick the adjusted (projected?) measurements off to use in my kinematics.

Alnwlsn: /* Software/The Math */

2019-08-19T12:36:12Z

Software/The Math

← Older revision		Revision as of 08:36, 19 August 2019
Line 41:		Line 41:
	q2 = atan(y/x) + atan((a2sin(-q1-pi))/(a1+a2cos(-q1-pi)));		q2 = atan(y/x) + atan((a2sin(-q1-pi))/(a1+a2cos(-q1-pi)));
	</pre>		</pre>

	where '''q1''' and '''q2''' are the angles shown on the GeoGebra model. We also have the other parameters of the arm, like the lengths of the arm segments('''a'''). Variables with a '''2''' after them are for the arm section, and ones with a '''1''' are for the forearm section. Our inputs are '''x''' and '''y''', which assumes that point '''A''' is at the origin and we want to place the end of the arm (point '''H''') at location (x,y).

	The last step in this is to tell us how we need to extend our actuators to get the angles we just found, which is found from the law of cosines:		The last step in this is to tell us how we need to extend our actuators to get the angles we just found, which is found from the law of cosines:
	</pre>		</pre>
	~~act1~~ = sqrt(l1^2+m1^2-2l1m1*cos(q1));		act2 = sqrt(l2^2+m2^2-2l2m2*cos(q1));
	~~act2~~ = sqrt(l2^2+m2^2-2l2m2cos(ng2(pi/180)-q2));		act1 = sqrt(l1^2+m1^2-2l1m1cos(ng2(pi/180)-q2));
	</pre>		</pre>
	~~Here, we need lengths along~~ the arm ~~segments where~~ the ~~actuators are mounted~~ (~~'''l'''~~ and ~~'''m''')~~, ~~which form~~ the ~~other 2 sides~~ of the ~~triangle we~~ are ~~calculating. Lastly~~, ~~we need~~ to ~~add in~~ the ~~angle at which~~ the ~~arm mount~~ is ~~tipped up~~ (~~'''ng'''~~)~~, so we get~~ the ~~right position.~~
			where:
			* q1 is the angle (radians) between the forearm and arm (at the top)
			* q2 is the angle (radians) between the arm and the horizon
			* x and y are Cartesian coordinates for where you want the end of the arm, with the origin at the arm shoulder
			* a1 and a2 are the lengths of the arm and forearm, respectively
			* m1 and l1 are the distances to the arm actuator mount points, measured from the shoulder bearing
			* m2 and l2 are the distances to the forearm actuator mount points, measured from the elbow bearing
			* ng2 is the angle (degrees) from the horizon to the line between the shoulder and lower actuator mount point

	That's pretty much it. We can just feed those actuator lengths into the controller for our actuator and the arm will position itself to the point that we want. However, this won't necessarily be a straight line move, because the actuators will just go at their own speeds. To fix this, I broke up the move into a bunch of tiny segments, and we command the arm to move to the endpoints of each segment, in sequence. To do this properly, we might first want to know the initial position of the arm. I use forwards kinematics for this, by recalculating the angles given the position of the arm actuators, and then the position of the end of the arm.		That's pretty much it. We can just feed those actuator lengths into the controller for our actuator and the arm will position itself to the point that we want. However, this won't necessarily be a straight line move, because the actuators will just go at their own speeds. To fix this, I broke up the move into a bunch of tiny segments, and we command the arm to move to the endpoints of each segment, in sequence. To do this properly, we might first want to know the initial position of the arm. I use forwards kinematics for this, by recalculating the angles given the position of the arm actuators, and then the position of the end of the arm.
	<pre>		<pre>
	~~q1b~~=acos((m1^2+l1^2-~~act1~~^2)/(2m1l1))		q1c=acos((m2^2+l2^2-act2^2)/(2m2l2));
	~~q2b~~=-acos((m2^2+l2^2-~~act2~~^2)/(2m2l2))+ng2*(pi/180)		q2c=-acos((m1^2+l1^2-act1^2)/(2m1l1))+ng2*(pi/180);
	x2=a1cos(pi-~~q1b~~-~~q2b~~)+a2cos(~~q2b~~)		x2=a2cos(pi-q1c-q2c)+a1cos(q2c)
	y2=a1sin(pi+~~q1b~~+~~q2b~~)+a2sin(~~q2b~~)		y2=a2sin(pi+q1c+q2c)+a1sin(q2c)
	</pre>		</pre>
	'''x2''' and '''y2''' are the position of the end of the arm. The idea is that we get the arm position from the actual reporting of the encoders, and therefore have a better idea of where the arm is, rather than assume it's in the spot we commanded it to go last time, in case I do ever want to control the arm manually.		'''x2''' and '''y2''' are the position of the end of the arm. The idea is that we get the arm position from the actual reporting of the encoders, and therefore have a better idea of where the arm is, rather than assume it's in the spot we commanded it to go last time, in case I do ever want to control the arm manually.

			''20190819 - The above formulas have been fixed. In my original version, I mixed up which arm was link 1 and link 2, but it still seemed to work. Now that I want to use links of different lengths, I've had to fix it.''

Alnwlsn: /* Encoders */

2019-08-18T00:23:36Z

Encoders

← Older revision		Revision as of 20:23, 17 August 2019
Line 14:		Line 14:

	==Encoders==		==Encoders==
	Yes, I made my own ~~engenders~~ for this project just like the ones I used on my wheelchair wheels. This is probably a bad idea and you should probably use of the shelf encoders. But, I don't want to wait for parts to arrive and I don't want to make any special adapters, and I again want to see if I can, so there you go.		[[File:Cow-encoders-test-v1.jpg\|thumb\|Linear actuators with the encoders installed, on a breadboard for testing.]]
			Yes, I made my own encoders for this project just like the ones I used on my wheelchair wheels. This is probably a bad idea and you should probably use of the shelf encoders. But, I don't want to wait for parts to arrive and I don't want to make any special adapters, and I again want to see if I can, so there you go.

	===Preparing the arm/forearm motors===		===Preparing the arm/forearm motors===

Alnwlsn: /* Encoders */

2019-08-16T04:05:10Z

Encoders

← Older revision		Revision as of 00:05, 16 August 2019
Line 14:		Line 14:

	==Encoders==		==Encoders==
			Yes, I made my own engenders for this project just like the ones I used on my wheelchair wheels. This is probably a bad idea and you should probably use of the shelf encoders. But, I don't want to wait for parts to arrive and I don't want to make any special adapters, and I again want to see if I can, so there you go.

			===Preparing the arm/forearm motors===
			Part of this project needs me to know how far the linear actuators are extended.
			There's no good way to attach an encoder to the linear actuators as is, you would probably have to use a big external linear displacement sensor, which sounds expensive. If I could just put a rotary encoder on the motor, I could figure out the displacement that way. It doesn't even have to be that high precision, because the gearing turns our few pulses into a few hundred over the span of the linear actuator.

			I decided to do this by extending the motor shaft out the back of the motor. To do this, I started with a section of 1/8 inch drill rod, which is the same size as the original shaft. The drill rod also has a pretty good outside diameter tolerance. Next, I replicate the features of the original shaft. At the end is a D shaped key on which the drive gear attaches; this was milled on the horizontal mill. Next, the middle of the shaft is knurled slightly, to make sure the motor armature has a nice press fit onto it. I then leave the rest of the new shaft as long as I want it to stick out the back of the motor.

			Now comes the tricky part. Very carefully, tap out the existing shaft from the armature. This is a press fit, but some of the armature pieces are made from easily squished plastic. Also, the commutator is not keyed to the armature by anything other than the shaft, so be very careful not to rotate it once the existing shaft is out. With the same care, the new long shaft can be tapped in.

			The last modification is in the motor end bell. Using a small drill, I put my drill through the rear bearing and carefully drilled through the cover. Then, the end bell can be flipped over and a larger than 1/8 drill used to enlarge the hole so the longer shaft can pass freely out of it. Be sure not to drill into the bearing when doing this, and clean out all the shavings afterwards.

			Add some oil to the bearings, and the modified motor can now be put back together. "But wait," I can hear you say, "Doesn't this mess up all the motor balances and such?" Well, yeah, technically. But these motors are not super precise to begin with, and I really haven't noticed much in the way of any extra vibration.

			So now the motors can be reinstalled in the linear actuator, but have the added benefit of an accessible shaft.

	==Software/The Math==		==Software/The Math==

Alnwlsn at 20:17, 14 August 2019

2019-08-14T20:17:07Z

← Older revision		Revision as of 16:17, 14 August 2019
Line 1:		Line 1:
	For this year's Winter Camp, Space is the theme. Therefore, after upgrading my electric wheelchair robot base this spring with [[RC Wheelchair 2\|a new motor controller]], I decided that it should also have a robotic arm, making it useful as a Mars rover - esque robot platform. The wheelchair base weights a hefty 100+ pounds, and I want this arm to be actually useful (ie, able to lift more than a tissue box). I have named it the '''Cow arm''', as it is designed to be beefier than those crummy kit arms that use servos.		For this year's Winter Camp, Space is the theme. Therefore, after upgrading my electric wheelchair robot base this spring with [[RC Wheelchair 2\|a new motor controller]], I decided that it should also have a robotic arm, making it useful as a Mars rover - esque robot platform. The wheelchair base weights a hefty 100+ pounds, and I want this arm to be actually useful (ie, able to lift more than a tissue box). I have named it the '''Cow arm''', as it is designed to be beefier than those crummy kit arms that use servos (Ok, well, it has to be called something).