Abstract
On the basis of hypothesis theories of linear elasticity and small deformation,the analytical compliance calculation formula of each sub-element in the compliance matrix of a right-circular flexure spherical hinge was deduced.The formula is succinct in form by introducing the proportional coefficient(The ratio of right-circular flexure spherical hinge groove spacing and double cutting radius)and utilizing the symmetrical feature of the structure.The correctness of the formula was verified by adopting the finite element simulation software,and its error curves were drawn corresponding to the simulated values.The results show that the relative errors of serial compliance calculation formula for the right-circular flexure spherical hinge are within 11% when the proportional coefficient is less than 0.2.With the increase of the proportional coefficient,the errors of the othercompliance calculation formulas have a trend of increasing with maximum of 30% except the error of tension and compression compliance C11 along the direction x.The experimental results show that the theoretical analysis is in agreement with the simulation results,which verifies the correctness of the proposed formula.These results will lay a key theoretical basis for the structural design and parametric optimization of the right-circular flexure spherical hinges in practical applications.
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