Kinematic Geometry of Surface Machining



Part Surfaces: Geometry
Elements of differential geometry of surfaces
On difference between classical differential geometry and engineering geometry
On classification of surfaces
Kinematics of Surface Generation
Kinematics of sculptured surface generation
Generating motions of the cutting tool
Motions of orientation of the cutting tool
Relative motions those causing sliding of a surface over itself
Feasible kinematic schemes of surface generation
On a possibility of the replacement of axodes with pitch surfaces
Examples of implementation of the kinematic schemes of surface generation
Applied Coordinate Systems and Linear Transformations
Applied coordinate systems
Coordinate system transformation
Useful equations
Chains of consequent linear transformations and a closed loop of consequent coordinate systems transformations
Impact of the coordinate systems transformations on fundamental forms of the surfaces
Part II: Fundamentals
The Geometry of Contact of Two Smooth Regular Surfaces
Local relative orientation of a part surface and of the cutting tool
The first order analysis: common tangent plane
The second order analysis
Rate of conformity of two smooth regular surfaces in the first order of tangency
Plücker’s conoid: more characteristic curves
Feasible kinds of contact of the surfaces p and t
Profiling Of the Form Cutting Tools of the Optimal Design
Profiling of the form cutting tools for sculptured surface machining
Generating of enveloping surfaces
Profiling of the form cutting tools for machining parts on conventional machine tools
Characteristic line of the part surface and of the generation surface of the cutting tool
Selection of the form cutting tools of rational design
The form cutting tools having continuously changeable the generating surface
Incorrect problems in profiling of the form cutting tools
Intermediate conclusion
Geometry of Active Part of a Cutting Tool
Transformation of the body bounded by the generating surface T into the cutting tool
Geometry of the active part of cutting tools in the tool-in-hand system
Geometry of the active part of cutting tools in the tool-in-use system
On capabilities of the analysis of geometry of the active part of cutting tools
Conditions of Proper Part Surface Generation
Optimal work-piece orientation on the worktable of multi-axis NC machine
Necessary and sufficient conditions of proper part surface generation
Global verification of satisfaction of the conditions of proper part surface generation
Accuracy of Surface Generation
Two principal kinds of deviations of the machined surface from
the nominal part surface
Local approximation of the contacting surfaces P and T
Computation of the elementary surface deviations
Total displacement of the cutting tool with respect to the part surface
Effective reduction of the elementary surface deviations
Principle of superposition of elementary surface deviations
Part III: Application
Selection of the Criterion of Optimization
Criteria of the efficiency of part surfaces machining
Productivity of surface machining
Interpretation of the surface generation output as a function of conformity
Synthesis of Optimal Surface Machining Operations
Synthesis of optimal surface generation: the local analysis
Synthesis of optimal surface generation: the regional analysis
Synthesis of optimal surface generation: the global analysis
On a possibility of the DG/K-based CAD/CAM system for optimal sculptured surface machining
Examples of Implementation of the Dg/K-Based Method of Surface Generation
Machining of sculptured surfaces on multi-axis NC machine
Machining of surfaces of revolution
Finishing of involute gears

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