1. A computer-implemented method for configuring a kinematic chain that represents an animated character, the method comprising: calculating a first recursion depth value associated with the kinematic chain, wherein the first recursion depth value represents a maximum length of a plurality of recursion paths; calculating a first output value based on a first solving order associated with the kinematic chain; identifying, based on the first recursion depth value, a first custom connection not included in the first solving order; in response, creating a second solving order associated with the kinematic chain, wherein the second solving order includes the first custom connection; calculating a second output value based on the first output value and the second solving order; performing one or more write operations that set a first angle in the kinematic chain based on the second output value; and generating animation data associated with the animated character based on the first angle in the kinematic chain.