Modeling a Walking Sequence

Hello, I am trying to model a walking sequence of a character in my game, here are the facts: - When the character is standing, the hip angle is 0 and the knee angle is 0; - For the angles, bending forward is positive, bending backward is negative; - Ignoring the ankle and toe, and assume that the length of thigh and calf are both 1, then the along-the-path displacement is therefore cos(HipAngle)+cos(HipAngle+KneeAngle); <<(right??) - The height displacement is sin(HipAngle)+sin(HipAngle+KneeAngle); - Assume that the function for HipR is fixed, and is sin(t), and the function for HipL is -sin(t); - Then the walking profile can be divided into 4 time intervals, with ThighR in frong during Inv1 and Inv2; The constraints: For the character to walk with exclusively either leg touching the ground, the height displacement of the Right Leg needs to exceed that of the Left Leg during Inv2 and Inv3; At the same time, the along-the-path displacement of the Right Leg must be decreasing during the interval Inv2 and Inv3; Explanation of the constraints: The begining of Inv2 begins at t=pi/2, when ThighR reached its most forward position. At that moment, the knee angle is approxmiately 0. Mathematically, both legs are touching the ground at that moment. After t=pi/2, the Right Leg pushes back, decreasing the along-the-path displacement, while the Left Leg lifts from the ground. The Right Leg keeps pushing until t=3pi/2, when the Left Thigh reached its most forward position. t=3pi/2 is the end of Inv3, thus, the height displacement of the Right Leg is greater than that of the Left Leg during Inv2 and Inv3. Problem: How do I solve for the equation of the Knee angles? thanks