Course detail
Kinematics
FSI-4KI-A Acad. year: 2027/2028 Summer semester
Kinematics, as a part of mechanics, is a science that deals with the motion of bodies irrespective of the forces causing the motion. Bodies have only the geometric properties that are constant. In kinematics, the body is immaterial; it is a model solid. The course covers the analysis of motions of a particle and rigid bodies. Topics include kinematics with absolute and relative motions of rigid bodies in translation, rotation, spherical and general planar motion using translating and rotating axes. Gained knowledge is applied to solving the mechanisms in motion. Mechanisms are solved both graphically and numerically. Kinematic geometry is applied as well.
Language of instruction
English
Number of ECTS credits
4
Supervisor
Entry knowledge
The student must be capable of solving the set of linear and quadratic equations. Trigonometry and analytic geometry. Calculus (differentiation and integration) in one variable. Vector algebra. Matrix algebra. Descriptive geometry.
Rules for evaluation and completion of the course
The course-unit credit is granted under the condition of active participation in seminars and passing the seminar tests of basic knowledge (at least 10 points out of 20 must be gained). The points gained in seminar tests are included in the final course evaluation.
Exam: The exam is divided into two parts. The first part consists of a comprehensive test, for which a maximum of 40 points can be earned. To proceed to the second part of the exam, students must earn at least 20 points on this test. If this requirement is not met, the exam is graded an F. The second part consists of written solutions to typical problems from the core areas of the course, for which a maximum of 40 points can be earned. The lecturer will provide details regarding the specific format of the exam, the types and number of problems or questions, and the grading criteria during the semester. The final grade is determined by the sum of the points earned in the seminars and on the exam. A minimum of 50 points is required to successfully complete the course.
Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge. Unexcused absences are grounds for failing to receive course-unit credit.
Aims
The course is aimed at proper formulation of motion definition, i.e. the students have to be able to determine how to set the position of a point, rigid body, or a system of rigid bodies, in any instant of time. On the basis of a position task solution other kinematic quantities (velocities and accelerations) are to be determined. Determination of the kinematic quantities is necessary for further dynamic solving. Computational methods are preferred.
The students will be able to analyse the movement from the point of view of kinematics and to perform the solution of motion variables determination. They will be able to analyse mechanisms, and on the basis of a set position determine the velocity and acceleration in arbitrary moment of time. As the matrix arithmetic is used during the analysis, the student will be able to solve kinematic problems using the computers.
The study programmes with the given course
Programme B-STI-A: Fundamentals of Mechanical Engineering, Bachelor's, compulsory
Programme B-STI-Z: Fundamentals of Mechanical Engineering, Bachelor's, recommended course
Type of course unit
Lecture
26 hours, optionally
Syllabus
1. Kinematics of a point; relationships between kinematic quantities
2. Orthogonal transformations of vector quantities. Translational motion of a body. Rotational motion of a body about a fixed axis of rotation
3. General planar motion, fundamental decomposition, pole of motion
4. General planar motion, acceleration of a point, example
5. Kinematic geometry
6. Combined motion, fundamental decomposition, example
7. Combined motion, matrix solution
8. Cam mechanisms, equivalent (supplementary) mechanisms, Coriolis method.
9. Simultaneous rotations, planetary mechanisms.
10. Methods for solving mechanisms, pole method, trigonometric method
11. Methods for solving mechanisms, vector method, matrix method
12. Spherical motion
13. Introduction to quaternions, sample exam.
Exercise
12 hours, compulsory
Syllabus
1. Rectilinear and curvilinear motion of a point
2. Rotation of a body
3. General planar motion
4. Combined motion
5. Cam mechanims
6. Planar mechanisms
Computer-assisted exercise
14 hours, compulsory
Syllabus
1. Rectilinear and curvilinear motion of a point.
2. Kinematics of a rigid body. Orthogonal transformations of kinematics quantities.
3. Absolute general plane motion, analytical analysis.
4. General spatial motion of a rigid body. Screw motion.
5.Relative motion analysis.
6.Coeval rotary motion, gears.
7. Analytical analysis of planar mechanisms.