Objective
The project consists in developing a mathematical theory which would enable the advantages and disadvantages of alternative mathematical representations for a specified geometry to be compared for any given orientation of the geometric form in the coordinate system of the measuring machine. This must inevitably relate uncertainty in the constants in the mathematical representation of any geometric form to the current position and orientation of the form in the coordinate system. In addition to leading to direct improvements in the uncertainties associated with data fits, it should be possible to give practical advice for the orientation of workpieces on 3 cmm when setting out to measure specific geometries. The following geometries have been considered in all orientations in an x-y-z coordinate system:
straight line (2d), straight line (3d), flat plane, circle (2d)
circle (3d), sphere, cylinder, cone
RESULTS
The theory developed describes how the above geometric elements can reliably be represented in terms of sets of algebraic parameters. For any element, it enables to determine whether a possible parameterisation is good or not and gives a quantitative measure for the degree of goodness.
Two sets of parametrisations are recommended. The first set applies to full elements, ie elements that are to be derived from measurements distributed throughout the feature. The second applies to partial elements derived from measurements over a relatively small portion of a feature. The parametrisation recommended is optimal or near-optimal in terms of the above measure.
Considerations have been given to the relationship between recommended parametrisation and algorithms used to determine numerical values of geometric element parameters. In addition, ways are recommended on how to algebraically represent the distance of a point from each of the main geometric elements, the formulae being given in terms of the recommended parameters.
A detailed description can be found in EUR Report 13517.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
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Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
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Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
TW11 0LW Teddington
United Kingdom
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.