In this work we present the kinematic model of an anthropomorphic hand, consisting of fingers with coupled joints similar to humans, for forward and inverse kinematics computation. Additionaly, a strategy for relative pose control between the finger tips and thumb is also developed. The formulation uses geometrical analysis, and the kinematic model can easily be integrated with the kinematics of a robotic arm in order to benefit from the added redundancy. The forward and inverse kinematic formulations use unit dual-quaternion representation of screw based kinematics which ensures singularity free representation of orientation. The model hence obtained is implemented on an anthropomorphic hand for validation.