Constructive processing of curves and surfaces

• Inženjerska grafika i mehatronika, Semester 1, position 1

The goal is for students to learn the basic geometric characteristics and invariants of plane and spatial curves, as well as surfaces important for mechanical engineering. The goal is also for students to master both theoretical and concrete, practical methods of generation and constructive processing of the mentioned types of curves and surfaces. Practical methods include the generation and processing of curves and surfaces by direct sketching and drawing procedures, as well as advanced methods that are implemented using appropriate computer tools (SolidWorks).

The outcome of the course is the acquisition of knowledge that can be applied in the generation and constructive processing of selected types of curves and surfaces that are used for designing and 3D modeling of various objects in the practice of mechanical engineering. By mastering this subject, students are trained to efficiently design and generate complex machine parts and assemblies.

Plane curved lines, order, class, degree and genus of algebraic curved lines; decomposition of algebraic curves; common points of curved lines; quadratic curves and their strands, projective properties of quadratic curves; asymptotes and singular points of curves; Plicker and Klein relations; flexion of plane curves, flexion and torsion of spatial curves; involute and involute of plane curves, involute of a circle - application in mechanical engineering; roulettes, epicycloids, hypocycloids - application in mechanical engineering; accompanying triad of spatial curves; spatial curves of 4 orders, 1st and 2nd types, spatial curve of 3rd order; surfaces, generation and division of surfaces, E, H, P surfaces; tangents, tangential planes and surface normals, curvature, principal curves and osculating paraboloid surfaces; Euler's theorem on surface curves and Mannheim constructions; Total curvature and developing surfaces and constructive procedures of developing parabolic surfaces of the second order; constructive processing of the cylindrical coil, various plane transcendental and algebraic curves created by projecting the coil: harmonic curves, hyperbolic spiral, roulettes, trochoids; chainworms and catenoids;

Exercises that are performed directly on paper, with the help of drawing accessories, as well as on computers with the use of appropriate software tools.

Passed courses Constructive geometry and graphics and Engineering graphics

Total assigned hours: 75

New material: 30
Elaboration and examples (recapitulation): 0

Auditory exercises: 30
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 5
Review and grading of the project: 0
Test: 5
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 30
Laboratory practice: 0
Calculation tasks: 30
Seminar paper: 0
Project: 0
Final exam: 40
Requirement for taking the exam (required number of points): 20

Laurent Busé , Fabrizio Catanese , Elisa Postinghel; Algebraic Curves and Surfaces A History of Shapes, Springer; 1st ed. 2023 edition