Planar Generalized Stewart Platforms and Their Direct Kinematics
نویسندگان
چکیده
In this paper, we introduce the concept of planar generalized Stewart platform (GSP) consisting of two rigid bodies connected with three constraints between three pairs of geometric primitives in the two rigid bodies respectively. This problem can be treated as a special but important class of geometric constraint solving problems. We show that there exist sixteen forms of planar GSPs. We also obtain the closedform solutions of the direct kinematics for the planar GSPs. For a class of GSPs with two distance and one angular constraints, we may give pure geometric solutions based on ruler and compass constructions.
منابع مشابه
Generalized Stewart Platforms and their Direct Kinematics
In this paper, we introduce the generalized Stewart platform consisting of two rigid bodies connected with six distance and/or angular constraints between six pairs of points, lines and/or planes in the base and moving platform respectively, which could be considered as the most general form of parallel manipulators with six DOF in certain sense. We prove that there exist 3850 possible forms of...
متن کاملNew Direct Kinematic Formulation of 6 D.O.F Stewart-Gough Platforms Using the Tetrahedron Approach
The paper presents a single constraint equation of the direct kinematic solution of 6-dof (Stewart-Gough) platforms. Many research works have presented a single polynomial of the direct kinematics for several 6-dof platforms. However, the formulation of the polynomial has potential problems such as complicated formulation procedures and discrimination of the actual solution from all roots. This...
متن کاملKinematic modeling of stewart-gough platforms
This paper describes a method to solve the direct kinematics of a generic Stewart-Gough manipulators. The method is formulated in terms of a search in the space of rigid body transformations. The underlying idea is that the solutions of the direct kinematics can be obtained by moving the end-effector body according rotations and translations and accounting for the rigidity conditions. The paper...
متن کاملSpecial issue on geometric constraints and reasoning
This special issue in CGTA follows the fourth edition of the special track: Geometric Constraints and Reasoning, in the 24th Annual ACM Symposium on Applied Computing, which took place in Honolulu, Hawaii, USA, March 9–12, 2009. Geometric Constraints and Reasoning is devoted to the recent trends in the domain of geometric constraint solving (GCS) and automated, or computer aided, deduction in g...
متن کاملA Distance-Based Formulation of the Octahedral Manipulator Kinematics
In most practical implementations of the Gough-Stewart platform, the octahedral form is either taken as it stands or is approximated. The kinematics of this particular instance of the Gough-Stewart platform, commonly known as the octahedral manipulator, has been thoughtfully studied. It is well-known, for example, that its forward kinematics can be solved by computing the roots of an octic poly...
متن کامل