FORWARD POSITION ANALYSIS OF NEARLY GENERAL STEWART PLATFORMS

This paper presents the closed-form solution of the forward position a nalysis of the nearly general stewart platform, which consists of a ba se and a moving planar platform connected by six extensible limbs thro ugh spherical joints in the two planar platforms. It becomes a general Stewart platform if the centers are not constrained to those two plan es. In this study, the coordinate transformation matrix is used to rep resent the position of the moving platform. Based on the six dependenc y equations of the rotation matrix and the six constraint equations re lated to the six link lengths, a set of six 4th degree equations in th ree unknowns are derived. Further derivations produce 21 dependent con straint equations. By simultaneous elimination of two unknowns a 20th order polynomial equation in one unknown is obtained. Due to dual solu tions of other unknowns, this indicates a maximum of 40 possible solut ions. The roots of this polynomial are then solved numerically and the realistic solutions are constructed using computer graphics.