Static Deformations Budget


Any motion of a rigid body in 3-D space is accompanied with six small deviations along and around its six DOF in infinitesimal motions. Sources of these errors are considered in detail as applied to geometrical errors [1]. For the 6-DOF manipulators, the total geometrical error vector depends on (6n + 6) components, where n is the number of links, among them only 6 errors are induced by actuated links. This approach is formulated through the variational method of accuracy calculation [2], which models any small displacement of the rigid body as a result of total variation of the nominal function (the form-shaping function [1, 2] fulfils the role of the nominal function as applied to machines and robots).

3.1Infinitesimal matrix-based approach
3.2Jacobian matrix of the deformation budget synthesis
3.3Synthesis of the compliance matrix
3.4Elastically supported chain of links: Compliance matrix synthesis
3.5Synthesis of the system stiffness matrix
3.6Structural deformations: FEM-based approach

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