A forward displacement analysis of a class of stewart platforms

✍ Scribed by Griffis, M. ;Duffy, J.

• Book ID: 112186888
• Publisher: John Wiley and Sons
• Year: 1989
• Tongue: English
• Weight: 931 KB
• Volume: 6
• Category: Article
• ISSN: 0741-2223
• DOI: 10.1002/rob.4620060604

✦ Synopsis

A closed-form forward displacement analysis is performed for a Stewart Platform-type of parallel mechanism, whose six legs meet in a pair-wise fashion at three points in the top and base platforms. The six legs and two platforms of this mechanism together form an octahedron. An eighth-degree polynomial in the square of the tan-half-angle that measures the elevation of a triangular face of the octahedron relative to the base triangle is derived. Each of three vertices of the base triangle of the octahedron is modeled by a spherical four-bar mechanism, and the polynomial is obtained by eliminating a pair of tan-half-angular displacements from the displacement equations of the three spherical four-bar mechanisms. The result are verified numerically by performing a reverse displacement analysis and displaying real solutions on a graphic system. It is clear that there are a maximum of eight reflected pairs of real assembly configurations of the octahedral form of the Stewart Platform.