Direct kinematic solution of a Stewart platform

The Stewart platform is a fully parallel, six-degree-of-freedom manipulator mechanism. A solution of the direct kinematics problem for the Stewart platform is presented for the case in which the six limbs form three concurrent pairs at either the base or the hand member. The solution is shown to be reducible to a 24th-order polynomial equation in tan(φ_r/2). It is also shown that, for a given set of link lengths, the Stewart platform can be assembled in 24 different configurations