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This is a simple case, representing a slider mechanism. Crank length Ra, connecting rod length Rb. Crank angle is given as ta. Then gudgen pin displacement from crank origin = x and conrod angle = tb

Resolving in x and one in y dirextions we have two equations in two unknowns. These should be simple to solve!

I tried the following on sagecell.sagemath.org:

Ra=0.5; Rb=3.0; ta=pi/2; var('x tb'); sol = solve([Racos(ta)+Rbcos(tb)==x, Rasin(ta)+Rbsin(tb)==0.0],x,tb,solution_dict=True) sol

[{3.0cos(tb): x}, {3.0sin(tb) + 0.5: 0.0}]

The result is oviously nonsense.

What am I doing wrong?

This is a simple case, representing a slider mechanism. Crank length Ra, connecting rod length Rb. Crank angle is given as ta. Then gudgen pin displacement from crank origin = x and conrod angle = tb

Resolving in x and one in y dirextions we have two equations in two unknowns. These should be simple to solve!

I tried the following on sagecell.sagemath.org:

Ra=0.5; Rb=3.0; ta=pi/2; var('x tb');
sol = solve([Racos(ta)+Rbcos(tb)==x, Rasin(ta)+Rbsin(tb)==0.0],x,tb,solution_dict=True)
sol
solve([Ra*cos(ta)+Rb*cos(tb)==x, Ra*sin(ta)+Rb*sin(tb)==0.0],x,tb,solution_dict=True)
sol
  
[{3.0cos(tb): [{3.0*cos(tb): x}, {3.0sin(tb) {3.0*sin(tb) + 0.5: 0.0}]0.0}]