@C_R gamma2 is in projective coordinates. Pgamma2 is conversion to Cartesian coordinates for plotting. I admit I could change gamma2 to gamma02, so using typeset(gamma2) would work.

@dharr Thank you. It worked once I also added the that to the Dual Document Propetties as well as the hyperlink.

@C_R Yes, Have tried switching the worksheet tab. The biggese irritation with these "new" hangs, is when quitting Maple it often does not offer the option to save your work. It used too. 

@nm Oh I use Maple every night. I have it happen when editing something small.

@acer  @Carl Love Both great contributions. The example I put up at the start was made up on the spot. Sqr and it's beloved alias XX was random. CircleParmUHG and eparm are genuine.
I picked  alias because that is all I knew about

The export suggestion. works very well. Part of the problem is, I have been tring to follow a naming convention in a set of lectrues. But over the past two years have come up with more extensive procedures placed in the top level package or give them different names. e.g. I have a command LPproj  which 1) converts a  list of Cartesian points to projective points, 2) joins two projective point to make a projective line vector, 3) meet of two line vectors to make a projective point, 4) checks if line and point are coincident, 5) converts a list of projective points back to Cartesian points 5) converts a list of line vectors to a*x +b*y +c and 6) converts a*x +b*y +c to <a,b,c> line vector.  I had an old command in the UHG module that did 2) and 3). That is used in quite a lot of my old documents.

Using export JFunction:=LPproj in the UHG module neatly handles having to convert all those old documents when I open them again.

@acer Opps...sorry about that. Interesting on alias not having to load the sub package. Is that just because the module is defined in the worksheet.? When I try this in the actual package i.e. with(RationalTrigonometry) the alias-es are not woking. 

If I can't get it working later, could you take a look? I would just inclued a couple of the simple commands in it. 

@acer @Carl Love Thank you for the answers. What would produce a FAIL as opposed to false? I don't think it will cause me a problem. I don't think speed/efficiency is super important here. It is part of a couple of plotting commands I use to make diagrams and that involves a lot of back and forth fiddling to get them to look ok. The check for the 1 is to draw the perpendicularity symbols between the lines and points.  e.g

@JAMET I appreciate that.

@JAMET You wanted to show that alpha is independant of the reference angle t. you showed it numerically. I was going after a proof. The reasoning being the the angle or parameter  t would eliminate from alpha for the claim to be true. I achieved that upto in signum terms. I only used alpha1 just to show the simplification of alpha. Yes I could have done alpha:=subs(......  , alpha). 

Now can you tell me the name of this theorem or point me to a reference on it? 

@one man  Nice platform model. I will have to find some time to sudy it.

@JAMET  Convert Setof to a list convert(Setof,list) and pick the one that has arcsin.

@JAMET Odd. There is nothing special in the code. It's all the usual Maple commands. Have you tried copy and paste sections of it?

I worked on that problem before

The reverse kinematics are quite straight forward. Here is a post I put up on that in 2017 Stewart Gough Reverse Kinematics - MaplePrimes 

The forward kinematics are best solved for all pratical purposes using numerical itteration. Use a Jacobian matrix for multi-variable itteration. See Jacobian - Maple Help (maplesoft.com) . 

@JAMET  Can you post a reference to some theorem on this? In general for problems like this I would not define the points and lines using the geometry package. That seems to require purely numerical values  .I can see that t is constant but t is in a form that takes on two values  theta and Pi- theta. That makes difficult to simplify alpha to eliminate t

What might help is rationally parameterising the point M on the ellipse  [a cos(t), b sin(t)] to [a* (1-lambda^2)/(1+lambda^2), b*2*lambda/(1+lambda^2)] ,    lambda=  -infinity to  +infinity. 

@vv Thanks. I was for some reason under the impression that there was no A3 format.