Solving equations

• To: mathgroup at smc.vnet.net
• Subject: [mg17104] Solving equations
• From: "Marcos Duarte" <mxd47 at psu.edu>
• Date: Sat, 17 Apr 1999 03:35:04 -0400
• Organization: Penn State University, Center for Academic Computing
• Sender: owner-wri-mathgroup at wolfram.com

```I'm trying to solve the following equations in Mathematica to find a
solution for a2 and a1:
x=d1*Cos[a1]+d2*Cos[a1+a2]
y=d1*Sin[a1]+d2*Sin[a1+a2]
These equations express the end-point position (x,y) of a two-link arm for a
planar case.

The answer (which are the angles (a1,a2) for a given (x,y)) is
straightforward:
a2=ArcCos[(x^2+y^2-d1^2-d2^2)/(2*d1*d2)]
a1=ArcTan[y/x]-ArcTan[(d2*Sin[a2])/(d1+d2*Cos[a2])]

But M. gets lost with all possible values that x,y,d1, and d2 can assume and
because of the use of inverse functions.
I also imposed the constraint that all the 4 parameters are different from
zero, but still I don't get anything close to the answer given above.

Does anybody have a solution?

--
Marcos Duarte
Biomechanics Lab      Pennsylvania State University
39 Rec. Building         University Park, PA   16801
Tel: 814 8653445    Fax: 814 8652440    Home: 814 8616157

```

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