The Stewart platform (SP) is a parallel closed‐kinematic chain robotic mechanism that is capable of providing high structural and positional rigidity. Because of its unique capability, the platforms have been employed in many control engineering applications such as simulator shakers, robotic manipulators, etc. However, a main problem often found in the implementation of a real‐time controller for the platform is the lack of an efficient algorithm for solving its highly nonlinear forward kinematic transformation (FKT), where one seeks to find the translational and orientational altitudes of the moveable platform from knowing the lengths of the platform linkages. This article describes two new direct and exact methods for computing the translational and rotational displacements of an SP by employing extra transnational displacement sensors (TDSs), in addition to the existing TDSs for the six links of the SP. The key for the approach lies in knowing where to employ the TDSs for determining positional vectors of strategic platform locations. By taking advantage of a tetrahedral geometry, closed‐form solutions for the FKT can then be derived and directly evaluated. The new methods produce accurate solutions with only minimal computation necessary. The advantages and disadvantages of the proposed methods are discussed and compared to an existing method. The exact methods are being investigated for an on‐line implementation of a nonlinear adaptive control system and redundancy scheme for a 25‐ton Stewart platform‐based Crew Station/Turret Motion Base Simulator (CS/TMBS) at the U.S. Army Tank‐Automotive Command (TACOM).

PAGE o 10.0 Base Line 20 mph 10.1 Non-Adaptive W/O Rebound Damping 20 mph 10.2 non-Adaptive 20 mph 10.3 Pitch Rate Adaptive 20 mph 10.4 Pitch Rate plus Heave Rate Adaptive 20 mph 11.0 Base Line 23 mph 11.1 Non-Adaptive W/0 Rebound Damping 25 mph 11.2 Non-Adaptive 25 mph 11.3 Pitch Rate Adaptive 25 mph 11.4 Pitch Rate plus Heave Rate Adaptive 25 mph 12.0 Base Line 30 mph 12.1 Non-Adaptive W/O Rebound Damping 30 mph 12.2 Non-Adaptive 30 mph 12.3 Pitch Rate Adaptive 30 mph 12.4 Pitch Rate plus Heave Rate Adaptive 30 mph 13.0 Base Line 35 mph 13.1 Non-Adaptive W/O Rebound Damping 35 mph 13.2 Non-Adaptive 35 mph 13.3 Pitch Rate Adaptive 35 mph 13.4 Pitch Rate plus Heave Rate Adaptive 35 mph 14.1 750 in-lb/deg 5 mph 14.2 900 in-lb/deg 5 mph 14.3 1100 in-lb/deg 5 mph SO hU o iv FIGURES cont'd PACE 14.4 2000 in-lb/deg 5 raph 15.1 750 in-lb/deg roph 15.2 900 in-lb/deg mph 15.3 1100 in-lb/deg 10 mph 15.4 2000 in-lb/deg 10 mph 16.1 750 in-lb/deg 15 mph 16.2 900 in-lb/deg 15 mph 16.3 1100 in-lb/deg 15 mph 16.4 2000 in-lb/deg 15 mph 17.1 in-lb/deg mph 17.2 in-lb/deg 20 mph 17.3 1100 in-lb/deg 20 roph 17.4 2000 in-lb/deg 20 mph 18.1 750 in-lb/deg 25 mph 18.2 900 in-lb/deg 25 mph 18.3 1100 in-lb/deg 25 roph 18.4 2000 in-lb/deg 25 roph 19.1 750 in-lb/deg 30 roph 19.2 900 in-lb/deg 30 roph 19.3 1100 in-lb/deg 30 roph 19.4 2000 in-lb/deg 30 mph 20.1 39* Road Arm Angle 5 mph 20.2

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