1. An Analytical Algorithm for a Seven-DOF Limb Real-time inverse kinematics techniques for anthropomorphic limbs Deepak Tolani, Ambarish Goswami, Norman I. Badler University of Pennsylvania

2. A 7 (or 4) degree-of-freedom limb Numerical approaches : Jacobian singularites, local minima Analytical approaches : efficient and reliable 3 DOF 1 DOF S1 S2 F L1 L2 L3

3. Inverse Kinematics Rotation matrices at joints S1, F, and S2 2 constant transformation matrices A desired goal The equation to solve

4. Step 1: Solving for Only affects the distance of S2 relative to S1. If the normal vector of the plane containing S1, S2, and F is parallel to the axis of rotation of F, then can be computed trivially using the law of cosines. Else, …

5. Step 2: Solving for Elbow Position

7. Step 3: Solving for R1 and R2

9. Class PV_IK \\vrs4\opensources\xmath \\vrs4\opensources\ik #include pv_ik.h … float t4, r1[4][4]; … PV_IK ik(L1, L2); ik.setGoal(gx, gy, gz); ik.solve(); //or ik.solve(psi); t4 = ik.getTheta4(); ik.getR1(r1);