🚀 go-pugleaf

In article <1992Aug12.171255.13584@morgan.ucs.mun.ca> raghu@morgan.ucs.mun.ca
(Raghu B) writes:
>Can any one tell me [...] where I can find the singular points for a PUMA-560
>arm. [...] Is there any algorithm or any set of equations which can be solved
>to get those arm joint angles theta1, theta2 and theta3.

The PUMA has three singularities: the ``alignment'' singularity
(wrist is as close to the axis of joint 1 as it can get),
the ``elbow'' singularity (elbow is fully extended or folded
up; the latter is not possible because of joint limits), and
the wrist singularity (the axes of joints 4 and 6 are aligned).

The angles corresponding to these depend on the DH parameter assignment.
For the PUMA, the definitions given in [1] are perhaps the most commonly used
(and I _think_ are what Unimation uses). Using these, and letting A2, A3, D3,
and D4 denote the translational DH offsets, the singularities occur when the
following are true: 

Alignment:	D4*sin(ang2+ang3) + A2*cos(ang2) - A3*cos(ang2+ang3) == 0

Elbow:		sin(ang3 - atan2(A3,D4)) == 0

Wrist:		sin(ang5) == 0

Typical offset values for the PUMA 560 are

A2 =  431.80
D3 =  149.09
A3 =  20.32
D4 =  433.070	

Hope this is helpful,

John Lloyd			Research Center for Intelligent Machines
lloyd@curly.mcrcim.mcgill.edu   McGill University, Montreal
(514) 398-8281			Fax: (514) 398-7348

[1] Richard Paul, Brian Shimano, and Gordon Mayer, ``Kinematic Control 
    Equations for Simple Manipulators''. IEEE Transactions on Systems,
    Man, and Cybernetics, Vol SMC-11, No. 6, June 1981.