Solving trignometric simultaneous equations

  • Thread starter peteculmer
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  • #1
Solving trignometric simultaneous equations....

Hi,

I'm in need of some help solving a set of simultaneous equations which will (hopefully!) solve the inverse kinematics for a robot arm. The equations are as follows:

eq1 := Xu-Xl = -c[4]*L_u2-s[4]*c[5]*L_l*c[6]-c[4]*L_l*s[6]+c[4]*L_u1

eq2 := Zu-Zl = c[3]*s[4]*L_u2-(c[3]*c[4]*c[5]-s[3]*s[5])*L_l*c[6]+c[3]*s[4]*L_l*s[6]-c[3]*s[4]*L_u1

eq3 := Yl = (s[3]*c[4]*c[5]+c[3]*s[5])*L_l*c[6]-Yu*(-L_u1+L_l*s[6])/L_u2

where s[3] denotes sin(theta3) and c[3] cos[theta3] etc

The unknowns I am trying to solve for are theta3,theta4 and theta5.
I have been attempting to use the solve command in maple but to no effect. If anybody has any pointers of what I could try,either methods or different packages etc I would be very grateful,
Thanks
Pete Culmer

EDIT:

I should point out that all other variables in the equations are known. I'm fairly sure there should be one or more symbolic solution(s)...hmmmm
 
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Answers and Replies

  • #2
dextercioby
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Advice:drope it dead.These are transcendental equations.Even if u'd be expressing everything in terms of "sines" (par éxample),it would be a system of irrational equations (involving radicals from unknowns).And besides,the number of equations is much less than the number of unknowns.

Daniel.
 

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