MTH503 Computer-Aided Analysis of Mechanical Systems of Machines

Code MTH503
Name Computer-Aided Analysis of Mechanical Systems of Machines
Status Compulsory/Courses of Limited Choice
Level and type Post-graduate Studies, Academic
Field of study Mechanics, Mechanical Engineering, Machine Building
Academic staff Jānis Auziņš, Aleksandrs Januševskis
Credit points 4.0 (6.0 ECTS)
Parts 1
Annotation Matrix methods in mechanism kinematics and dynamics. The method of constraints for planar kinematic analysis. Revolute, prismatic, gear and cam pairs are considered together with other 2 degrees-of-freedom types of constraints. Formal description of kinematic diagrams. The automatic assembly of the systems of equations for position, velocity and acceleration analysis. Geometry of masses. Forward and inverse tasks of geometric, statistic, kinematic and dynamic analysis. Dynamics of planar systems. Computation of planar generalized forces for external forces and for actuator-spring-damper element. Relations between transfer velocity, angular velocity of rigid body and generalized velocities: analogue matrices. Simple applications of inverse and forward dynamic analysis. Numerical integration of first-order initial-value problems. Accuracy and stability of integration methods. Kinematics of rigid bodies in space. Reference frames for the location of a body in space. Euler angles and Euler parameters. Velocity, acceleration and angular velocity. Relationship between the angular velocity vector and the time derivatives of Euler parameters. Kinematic analysis of spatial systems. Basic kinematic constraints. Joint definition frames. Denavit-Hartenberg notation. The constraints required for the description in space of common kinematic pairs (revolute, prismatic, cylindrical, spherical). Equations of motion of constrained spatial systems. Computation of spatial generalized forces for external forces and for actuator-springdamper element. Computation of reaction forces from Lagrange’s multipliers. .
Dynamical models of AC and DC electromotors, internal-combustion and diesel engines. Dynamical models of control systems: PID controllers. .
2D simulation packages: Working model 2D..
3D simulation packages MSC ADAMS: ADAMS View..
Parametric optimization.Programs ADAMS Insight, EDAOpt..
Goals and objectives
of the course in terms
of competences and skills
Develop knowledge and skills of basic mechanism and machine analysis. Develop understanding of various classes of linkages. Develop understanding of kinematics and dynamics of rigid bodies in mechanism chains. Develop understanding of forward and inverse kinematic and dynamic problems. Develop understanding of the basics of numerical integration for machine dynamic simulation. Develop knowledge of machine drive and control system simulation. Develop ability to perform position, velocity, acceleration and force analysis on 2D and 3D mechanisms and machines by use of commercial software. Develop understanding of how to analyze machines and how to properly report the results.
Learning outcomes
and assessment
Knowledge of vector and matrix mathematics for the analysis of mechanisms. - Exam questions
Knowledge of common elements in machine design. - Exam questions
Ability to perform kinematic analysis of mechanisms. - Independent task/work
Ability to perform dynamic simulation of machines. - Independent task/work
Ability to apply numerical integration methods. - Independent task/work
Proficiency to apply software to solve engineering problems including ODE's, systems of linear equations, and eigenvalue analysis. - Independent task/work
Compute kinematics and dynamics of 3D mechanisms using Euler angles, Euler parameters, rotation matrices, constraint vectors. - Coursework
Ability to develop and utilize models of machines. - Exam questions
Ability to optimize of machines. - Coursework
Use of commercially available mechanism analysis software and understand the underlying algorithms and theory behind them. - Coursework
Course prerequisites Mathematics, physics, mechanics, Theoretical mechanics.

[Extended course information PDF]