tailieunhanh - Advanced Strategies For Robot Manipulators Part 15

Tham khảo tài liệu 'advanced strategies for robot manipulators part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Structure and Property of the Singularity Loci of Gough-Stewart Manipulator 411 I Z f2XZ2 f3YZ2 f4X2Z f5Y2Z f6XYZ f7Z2 f8X2 f9Y2 f10XY fuXZ f12YZ f13Z f14X f15Y f16 0 42 where X Y Z are the coordinates of center point P. It is a polynomial expression of degree three. The equation is still very complicated and difficult to further analyze but it is very simple in the following special cases. When 30 90 and 150 and y is one of the values 30 90 or 150 Eq. 42 degenerates into a plane and a hyperbolic paraboloid as well. For example wheny 90 the singularity equation is 2Z Rb sin0 auX2 a22Y2 a33Z2 2a23YZ 2a31ZX 2a12XY 2a14X 2a24Y 2a34Z a44 0 43 where these coefficients are listed in the Appendix 2. Eq. 43 indicates a plane and a hyperbolic paraboloid. The first factor forms a plane equation 2Z Rbsin0 0 44 which is parallel to the basic plane. When point P lies in the plane the mechanism is singular for orientation Ộ 0 90 because points B3 and B5 lie in the basic plane. This is similar to Case 6. All the six lines cross the same line C1C2. Singularity analysis using singularity-equivalent-mechanism The singularity locus expression Eq. 43 for general orientations has been derived by Theorem 3. But it is still quite complicated and we are not sure whether it consists of some typical geometrical figures. Meanwhile the property of singularity loci is unknown yet. In order to reply this question a Singularity-Equivalent-Mechanism which is a planar mechanism is proposed. Thus the troublesome singularity analysis of the GSP can be transformed into a position analysis of the simpler planar mechanism. The parallel case The Singularity-Equivalent-Mechanism In the parallel case the three Euler angles of the mobile platform are 90 0 y while 0 and y can be any nonzero value. The mobile plane of the mechanism lies on 0-plane Fig. 5 . The corresponding imaginary planar singularity-equivalent-mechanism is illustrated in Fig. 8. Where Rdenotes a revolute pair and P a .

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