Machine Dynamics

Description

The objectives of this subject are to give students an understanding of the kinematics and dynamics of rigid bodies in general planar motion, which is typically encountered in design and analysis of mechanical systems, and an elementary understanding of the vibration of mechanical systems, in particular the dynamic behaviour of single-degree-of-freedom mechanical systems with various damping and applied forces. Students should be able to: model problems in rigid body planar and spatial kinematics and rigid body planar dynamics; understand energy methods in contrast to direct applications of Newton's second law of motion for setting up a model; understand the physics of a problem formulated from a real mechanical system; appreciate the role of vibration in machines and structures in the engineering world; understand the procedures required to evaluate a vibration problem; and analyse the dynamic response of single-degree-of-freedom mechanical systems. The subject also covers the concept of a rigid body, full nomenclature used in kinematics, two-body velocity equations and velocity diagrams of planar motion; two-body acceleration equations and acceleration diagram; three-body velocity equations and acceleration equations including Coriolis acceleration term; angular velocity acceleration equations including three-dimensional problems; F=ma applied to a rigid-body-dynamics, significance of 'centre of mass', the 'moment' relationship (M=Ia, etc.); angular momentum, conservation of angular momentum (general case, centre of mass moving, no 'fixed' point); linear and angular impulse problems; energy methods for general planar motion; elementary principles of vibration theory, free vibration of undamped single-degree-of-freedom system; free decay vibration of damped single-degree-of-freedom system; and the forced vibration of single-degree-of-freedom system.

Subject objectives

Upon successful completion of this subject students should be able to:

1. Illustrate basic mechanics concepts such as rigid body, force, motion, work, energy, power, impulse and momentum, and the relationships between them

2. Break down a simple machine or a mechanical system into a series of rigid bodies and evaluate the kinematics and kinetics between them

3. Apply velocity and acceleration equations of a rigid body in planar motion for determining its motion status, including angular velocity and acceleration, and linear velocity and acceleration of its any given points

4. Explain Newtonian mechanics, the relationships between the forces/moments and accelerations of a rigid body in planar motion; the velocities and work, & energies of a rigid body, or rigid bodies; and the relationships between linear/angular momentums and impulses

5. Apply the above kinematics and kinetics theories to model and quantify the various physical processes such as a rigid body?s dynamic states at each instant in relation to external forces, the state changes between two instants and impact problems between rigid bodies. (These are the core activities of practical mechanical engineering work.)

This subject also contributes specifically to the development of the following course intended learning outcomes:

Apply systems thinking to understand complex system behaviour including interactions between components and with other systems (social, cultural, legislative, environmental, business etc.) [EA Stage 1 Competency: 1.5 ] (A.5)

Identify and apply relevant problem solving methodologies [EA Stage 1 Competency:1.1, 2.1, 2.2, 2.3] (B.1)

Design components, systems and/or processes to meet required specifications [EA Stage 1 Competency: 1.3, 1.6, 2.1, 2.2, 2.3] (B.2)

Demonstrate research skills [EA Stage 1 Competency: 1.4, 2.1] (B.6)

Develop models using appropriate tools such as computer software, laboratory equipment and other devices [EA Stage 1 Competency: 2.2,2.3, 2.4] (C.2)

Evaluate model applicability, accuracy and limitations [EA Stage 1 Competency: 2.1,2.2] (C.3)

Communicate effectively in ways appropriate to the discipline, audience and purpose [EA Stage 1 Competency: 3.2] (E.1)

Teaching and learning strategies

This subject includes three hours of lecture and 1.5 hours tutorial per week throughout the semester.

As a student in this subject you are expected to attend lectures and tutorials, actively contribute to discussions, complete your assignments by their due dates and participate fully in your group for any group projects.

NOTE: As an indication, a typical 6cp subject would normally assume a total time commitment (including class time) of approximately 150 hours, for an average students aiming to pass the subject).

Content

The subject contents are:

revision on the kinematics of particles;

the kinematics of rigid bodies including absolute velocity and acceleration of rigid bodies in translation, fixed axis rotation, and general planar motions, concepts of velocity pole and introduction to spatial kinematics;

kinetics of rigid bodies including the relationships between forces and motions (Newton?s 2nd law of motion), energy, work, power, principle of energy conservation, linear and angular impulses, and momentums equations;

introduction to free vibration of a single degree of freedom mechanical system

Assessment

Assessment task 1: Kinematics of Rigid Body - Velocity Equations

Objective(s):

This assessment task addresses subject learning objectives:

1, 2, 3 and 5

This assessment task contributes to the development of the following course intended learning outcomes:

A.5, B.1, C.2, C.3 and E.1

Type: Quiz/test

Groupwork: Individual

Weight: 11%

Criteria linkages:

Criteria Weight (%) SLOs CILOs

Correctness of calculations 13 1, 2, 3 A.5, B.1, C.2, C.3, E.1

Clarity of kinematic diagram(s) 13 1, 2, 3, 5 A.5, B.1, C.2, C.3, E.1

Completeness of kinematic diagram(s) 13 1, 2, 3, 5 A.5, B.1, C.2, C.3, E.1

Understanding and application of analysis methods for determining the velocity of a rigid body undergoing general plane motion 13 1, 2, 3, 5 A.5, B.1, C.2, C.3

Justification of equations 13 1, 2, 3, 5 A.5, B.1, C.2, C.3

Correct use of units and significant figures 13 1, 2, 3 A.5, B.1, C.2, C.3, E.1

Conjecturing alternatives 13 1, 2, 3 A.5, B.1, C.2, C.3

Neatness 9 1 E.1

SLOs: subject learning objectives

CILOs: course intended learning outcomes

Assessment task 2: Kinematics of Rigid Body - Acceleration Equations

Objective(s):

This assessment task addresses subject learning objectives:

1, 2, 3 and 5

This assessment task contributes to the development of the following course intended learning outcomes:

A.5, B.1, C.2, C.3 and E.1

Type: Quiz/test

Groupwork: Individual

Weight: 11%

Criteria linkages:

Criteria Weight (%) SLOs CILOs

Correctness of calculations 13 1, 2, 3, 5 A.5, B.1, C.2, C.3, E.1

Clarity of kinematic diagram(s) 13 1, 2, 3, 5 A.5, B.1, C.2, C.3, E.1

Completeness of kinematic diagram(s) 13 1, 2, 3, 5 A.5, B.1, C.2, C.3, E.1

Understanding and application of analysis methods for determining the acceleration of a rigid body undergoing general plane motion 13 1, 2, 3, 5 A.5, B.1, C.2, C.3

Justification of equations 13 1, 2, 3, 5 A.5, B.1, C.2, C.3

Correct use of units and significant figures 13 1, 2, 3 A.5, B.1, C.2, C.3, E.1

Conjecturing alternatives 13 1, 2, 3 A.5, B.1, C.2, C.3

Neatness 9 1 E.1

SLOs: subject learning objectives

CILOs: course intended learning outcomes

Assessment task 3: Kinetic Equation of Motion - Translation and Fixed Axis Rotation

Objective(s):

This assessment task addresses subject learning objectives:

1, 2, 4 and 5

This assessment task contributes to the development of the following course intended learning outcomes:

A.5, B.1, C.2, C.3 and E.1

Type: Exercises

Groupwork: Individual

Weight: 5%

Criteria linkages:

Criteria Weight (%) SLOs CILOs

Correctness of calculations 10 1, 2, 4, 5 A.5, B.1, C.2, C.3, E.1

Clarity of free-body diagrams 10 1, 2, 4, 5 A.5, B.1, C.2, C.3, E.1

Completeness of free-body diagrams 10 1, 2, 4, 5 A.5, B.1, C.2, C.3, E.1

Clarity of kinetic diagrams 10 1, 2, 4, 5 A.5, B.1, C.2, C.3, E.1

Completeness of kinetic diagrams 10 1, 2, 4, 5 A.5, B.1, C.2, C.3, E.1

Understanding and application of planar kinetic equation of motion to rigid bodies undergoing translation and rotation about a fixed axis 10 1, 2, 4, 5 A.5, B.1, C.2, C.3

Justification of equations 10 1, 2, 4, 5 A.5, B.1, C.2, C.3

Correct use of units and significant figures 10 1, 2, 4 A.5, B.1, C.2, C.3, E.1

Conjecturing alternatives 10 1, 2, 4 A.5, B.1, C.2, C.3

Neatness 10 1 E.1

SLOs: subject learning objectives

CILOs: course intended learning outcomes

Assessment task 4: Kinetic Equation of Motion - General Planar Motion

Objective(s):

This assessment task addresses subject learning objectives:

1, 2, 3, 4 and 5

This assessment task contributes to the development of the following course intended learning outcomes:

A.5, B.1, B.2, C.2, C.3 and E.1

Type: Quiz/test

Groupwork: Individual

Weight: 11%

Criteria linkages:

Criteria Weight (%) SLOs CILOs

Correctness of calculations 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Clarity of free-body diagrams 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Completeness of free-body diagrams 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Clarity of kinetic diagrams 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Completeness of kinetic diagrams 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Understanding and application of planar kinetic equation of motion to rigid bodies undergoing general plane motion 10 1, 2, 3, 4, 5 A.5, B.1, B.2, C.2, C.3

Justification of equations 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3

Correct use of units and significant figures 10 1, 2, 3, 4 A.5, B.1, C.2, C.3, E.1

Conjecturing alternatives 10 1, 2, 3, 4 A.5, B.1, C.2, C.3

Neatness 10 1 E.1

SLOs: subject learning objectives

CILOs: course intended learning outcomes

Assessment task 5: Work and Energy Equations & Linear and Angular Momentum Equations

Objective(s):

This assessment task addresses subject learning objectives:

1, 2, 3, 4 and 5

This assessment task contributes to the development of the following course intended learning outcomes:

A.5, B.1, B.2, B.6, C.2, C.3 and E.1

Type: Quiz/test

Groupwork: Individual

Weight: 12%

Criteria linkages:

Criteria Weight (%) SLOs CILOs

Correctness of calculations 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Clarity of free-body diagrams 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Completeness of free-body diagrams 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Clarity of kinematic diagrams 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Completeness of kinematic diagrams 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Understanding and application of the principle of work and energy and the principles of linear and angular impulse and momentum 10 1, 2, 3, 4, 5 A.5, B.1, B.2, B.6, C.2, C.3

Justification of equations 10 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3

Correct use of units and significant figures 10 1, 2, 3, 4 A.5, B.1, C.2, C.3, E.1

Conjecturing alternatives 10 1, 2, 3, 4 A.5, B.1, C.2, C.3

Neatness 10 1 E.1

SLOs: subject learning objectives

CILOs: course intended learning outcomes

Assessment task 6: Final Exam

Objective(s):

This assessment task addresses subject learning objectives:

1, 2, 3, 4 and 5

This assessment task contributes to the development of the following course intended learning outcomes:

A.5, B.1, B.2, B.6, C.2, C.3 and E.1

Type: Examination

Groupwork: Individual

Weight: 50%

Criteria linkages:

Criteria Weight (%) SLOs CILOs

Correctness of calculations 8 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Clarity of free-body diagrams 8 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Completeness of free-body diagrams 8 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Clarity of kinematic diagrams 8 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Completeness of kinematic diagrams 8 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Clarity of kinetic diagrams 8 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Completeness of kinetic diagrams 8 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3, E.1

Understanding and application of kinematics and kinetics theories of rigid bodies 8 1, 2, 3, 4, 5 A.5, B.1, B.2, B.6, C.2, C.3

Justification of equations 8 1, 2, 3, 4, 5 A.5, B.1, C.2, C.3

Correct use of units and significant figures 8 1, 2, 3, 4 A.5, B.1, C.2, C.3, E.1

Conjecturing alternatives 8 1, 2, 3, 4 A.5, B.1, C.2, C.3

Neatness 12 1 E.1

SLOs: subject learning objectives

CILOs: course intended learning outcomes

Minimum requirements

In order to pass the subject, you must

attempt, complete, and submit each of the Assessment tasks 1-5; and

receive 50% from the final informal exam; and

earn an overall total of 50 marks or more for the subject