How can I perform a recursive input using the solve 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.

Answer 1

[Walter Roberson]

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)

[Evan Anderson]

Thanks for this. I ended up being able to use a while loop pretty easily, I just had to rearrange some things. Any and all help was appreciated!