🚀 go-pugleaf

In article <1992Aug12.171255.13584@morgan.ucs.mun.ca> raghu@morgan.ucs.mun.ca (Raghu B) writes:
>Can any one tell me any reference books are any valuable materials,
>from where I can find the singular points for a PUMA-560 arm.
>I know that they are the extreme ends of the workspace. But
>I don't know how to find those values. Is there any algorithm
>or any set of equations which can be solved to get those arm
>joint angles theta1, theta2 and theta3.

I'm assuming you're just interested in positioning, though there
is a wrist singularity as well.

Craig looks at the PUMA to some extent.  

Joel Burdick, in his thesis, shows how to find the singularities
of a general 3R positional manipulator (pp. 42--70; pp. 87--100).

Using DH parameters which place the zero position as the
arm straight over head (differing from Craig, and from Unimation...),
the following apply:

There are two boundaries, the external workspace boundary, 
which is when sin(theta3) = 0, (or theta3 = 0 degrees, since
-180 is not possible due to joint limits)
and the other is the internal workspace boundary
which is when the origin of frames 4-6 are directly over
the axis of frame 1 (assuming I'm numbering these correctly...)
which is when l2 * cos(theta2) + l3 * cos(theta2 + theta3) = 0.

You will have to do the trig to convert to Unimation's or
Craig's versions of DH parameters...

The (wristless) PUMA is an elbow manipulator; these formulas are 
generic for elbow manipulators (Z1 intersects Z2 at 90 degrees,
and Z3 is parallel to Z2).

Note that there is no dependence on theta1 - that is, if (a1, a2, a3)
is a set of joint angles which is a singular point, then (x, a2, a3)
will also be a singular point for any x within the joint limits of
joint 1.

Hope this helps.

Dave


-- 
Dave DeMers			 ddemers@UCSD   demers@cs.ucsd.edu
Computer Science & Engineering	C-014		demers%cs@ucsd.bitnet
UC San Diego					...!ucsd!cs!demers
La Jolla, CA 92093-0114	(619) 534-0688, or -8187, FAX: (619) 534-7029