MATLAB: How to perform a recursive input using the solve function

recursionsolve function

I've created some code to simulate a crank-rocker mechanism and I'm wondering how to perform an operation where I take the crank rotating 360 degrees and spit out all of the theta values for each corresponding link of the mechanism.
For reference: r1 = ground, r2 = crank, r3 = attachment link, r4 = rocker
t1, t2, t3, t4 are all thetas for reach respective link
Here is the code:
r1=4.2; r2=1; r3=5; r4=2.032;
t1=0; t2=0:1:360; 
syms t3 t4 positive
eqn1 = r2.*cosd(t2)+r3.*cosd(t3)==r1.*cosd(t1)+r4.*cosd(t4);
eqn2 = r2.*sind(t2)+r3.*sind(t3)==r1.*sind(t1)+r4.*sind(t4);
S = solve(eqn1, eqn2, 'IgnoreAnalyticConstraints', true)
When I run the code, it gives me 4 error messages:
Error using sym.getEqnsVars>checkVariables (line 92)
Second argument must be a vector of symbolic variables.
Error in sym.getEqnsVars (line 56)
checkVariables(vars)
Error in sym/solve>getEqns (line 429)
[eqns, vars] = sym.getEqnsVars(argv{:});
Error in sym/solve (line 226)
[eqns,vars,options] = getEqns(varargin{:});
I'm just looking to find a way to scale t2 from 0 to 360 degrees such that t3 and t4 give positive values only. I know how to do this with a single number, but once t2 becomes an array, I don't know how to solve those issues.

Best Answer

t1=0; t2=0:1:360;
So t2 is a vector of length 361
eqn1 = r2.*cosd(t2)+r3.*cosd(t3)==r1.*cosd(t1)+r4.*cosd(t4);
With t2 being a vector of length 361, the left hand side of the == is a vector. The right hand side is a scalar, but expansion will be done so that you will get a vector of equations, one for each element of t2.
Likewise, eqn2 will be a vector of equations.
 solve(eqn1, eqn2, 'IgnoreAnalyticConstraints', true)
with two vectors of length 361, would be trying to solve 722 simultaneous equations, in a total of two unknowns.
You are not going to be able to find a part of t3 and t4 values that manages to solve all 722 equations simultaneously .
You will need something like
 arrayfun(@(E1, E2) solve(E1, E2, [t3, t4], 'IgnoreAnalyticConstraints', true), eqn1, eqn2, 'uniform', 0)
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