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Hey guys, I would appreciate some help with the math behind creating a working coordinate system for a robotic arm. I am currently trying to determine what servo angles are necessary to align a robotic arm's claw to the given coordinates. Geometrically simplified, the robotic arm is a parallelogram with two servos at one vertex and one side extended further for the claw. Here is a diagram, pardon my drawing skills:

The sides marked

As for what I have tried, I have calculated the claw's coordinates to be

The sides marked

**D**are parallel and equivalent, as are the sides marked**C**.**E**is of fixed length and is attached to**C**(in reality it is just the extension of the**C**piece). The servos at bottom vertex**DC**adjust angles**a**and**b**to move sides**D**and**C**from the vertical. The claw itself is at the end of**E**, and**x**refers to the horizontal distance and**y**the vertical distance from the origin of the two angles**a**and**b**(AKA where the servos are placed).As for what I have tried, I have calculated the claw's coordinates to be

**X=D*sin(a)+E*sin(b)**and**Y=D*cos(a)-E*cos(b),**but I am unable to solve the system of equations such that I can determine what to set angles**a**and**b**to move the claw to a given point. When using substitution, I only end up with an extremely convoluted equation that my calculator cannot parse, leading me to believe I am going down the wrong path. Any help would be much appreciated!*(Also would like to mention for full transparency that this was cross posted to the Math Stack Exchange to no avail)*