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4 – FUNDAMENTALS bush

4 – FUNDAMENTALS bush and ball bearings or other bearing systems e.g. magnetic, hydrostatic, hydrody- namic and air guidings [4]. But they also have some disadvantages which are listed in the following compilation. Advantages Disadvantages Frictionless guiding Limited strokes No wear and therefore no wear debris Restoring forces No galling Complex geometries No lubrication High transversal rigidity No play Monolithic piece A conclusion of this valuation shows, that flexible hinges are ideal for the MSTS application due to the frictionless, lubrication and wear debris free guiding 3 . The reachable stroke will be determined by the design analysis discussed in chapter 5.4. Different translational and rotatory FH designs are presented with formulas in [4] and [6] with improvements of the general designs in [10] and [13]. Figure 4.1 shows three patterns of flexible hinges for getting a first impression in which direction the design of the MSTS FH structure tends. These designs have different advantages and disadvantages. For instance, the circular notch hinge features the highest precision due to its stationary rotation center. However, high forces must be applied for reaching adequate deflections. 4.1.2 Theory The formulas for calculating the forces and deflections, presented in the above men- tioned papers, are exclusively deduced form the fundamental theory of structural me- chanics y ′′ = M(x) EI(x) + η GA(x) ∂F (x) . (4.1) ∂x This equation describes approximately the curvature of a beam implementing the bending moment M, Young’s modulus E and the geometrical moment of inertia I. The term in the brackets describes the shearing, which won’t be further considered due to its small influence on the deflection [4]. 3 Applying lubricants in spacecraft mechanisms is generally problematic, especially inside optical instruments. As well as wear debis, they can contaminate the optical components. 12

a) b) c) 4 – FUNDAMENTALS Figure 4.1: General designs of flexible hinges: a) leaf spring hinge, b) circular notch hinge and c) elliptical notch hinge [6]. The mathematical description in (4.1) bases on three assumptions named continu- ity, homogeneity and isotropy. Parts of the MSTS FH structure can possibly reach dimensions where some of these assumptions loose validity due to very thin waists. Therefore, a good knowledge about the material properties and the accuracy of the FEM calculations is required for the MSTS FH design. 4.1.3 Materials A lot of materials, preferably metals, are applicable for flexible hinges. Thereby, different properties like • density, • Young’s modulus, • endurance strength, • thermal conductivity, • space qualification and • radiation degradation must be evaluated. The range of applicable materials is not only limited to metals as already shown with the mentioned MEMS sensor. Also ceramics like silicon nitride (Si3N4) or composits 13

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