
Unit 4: 
Mechanical Principles 


Unit code:

F/601/1450



QCF level:

5



Credit value:

15






• Aim
This unit aims to develop learners’ understanding of an extended range
of mechanical principles that underpin the design and operation of mechanical engineering
systems.
• Unit abstract
This unit will develop learners’ understanding of complex loading
systems and will provide an introduction to the concept of volumetric strain
and the relationship between elastic constants. The expressions derived for
linear and volumetric strain then form a basis for determining dimensional
changes in loaded cylinders.
The unit will build upon learners’ existing knowledge of the
relationship between the distribution of shear force and bending moment in
loaded beams, to include the relationship between bending moment, slope and
deflection.
Learners
will analyse the use of mechanical power transmission systems, both
individually and in the combinations that are used in practical situations.
Learners’ knowledge of rotating system elements is further extended through an
investigation of the dynamic characteristics of the slidercrank and fourbar
linkage. The balancing of rotating systems is also investigated, together with
the determination of flywheel mass and size to give sufficiently smooth
operating conditions.
• Learning outcomes
On successful completion of this unit a
learner will:
1 Be able to determine the behavioural
characteristics of materials subjected to complex loading systems
2 Be able to determine the behavioural
characteristics of loaded beams and cylinders
3 Be able to determine the dynamic parameters
of power transmission system elements
4 Be able to determine the dynamic parameters
of rotating systems.
Unit content
1
Be able
to determine the behavioural characteristics of materials subjected to complex
loading systems
Relationship: definition of Poisson’s Ratio; typical values of Poisson’s Ratio for
common engineering materials
Two and threedimensional loading: expressions for strain in the x, y and
zdirections; calculation of changes in dimensions
Volumetric
strain: expression for
volumetric strain; calculation of volume change
Elastic constants: definition of Bulk Modulus; relationship between Modulus of Elasticity;
Shear Modulus; Bulk Modulus and Poisson’s Ratio for an elastic material
2 Be able to determine the behavioural
characteristics of loaded beams and
cylinders
Relationships: slope i = ^{1} _{∫}Mdx
E1
deflection
y = _{E}^{1}_{1} _{∫∫} Mdxdx
Loaded beams: slope and deflection for loaded beams eg
cantilever beams carrying a concentrated load at the free end or a
uniformly distributed load over the entire length, simply supported beams
carrying a central concentrated load or a uniformly distributed load over the
entire length
Stresses in
thinwalled pressure vessels: circumferential hoop stress and longitudinal stress in
cylindrical and spherical pressure vessels subjected to internal and external
pressure eg compressedair receivers, boiler steam drums, submarine hulls,
condenser casings; factor of safety; joint efficiency
Stresses in
thickwalled cylinders:
circumferential hoop stress, longitudinal stress and radial stress in
thickwalled cylinders subjected to pressure eg hydraulic cylinders, extrusion
dies, gun barrels; Lame’s theory; use of boundary conditions and distribution
of stress in the cylinder walls
3
Be able
to determine the dynamic parameters of power transmission system elements
Belt drives: flat and vsection belts; limiting coefficient friction; limiting
slack and tight side tensions; initial tension requirements; maximum
power transmitted
Friction
clutches: flat single and
multiplate clutches; conical clutches; coefficient of friction; spring
force requirements; maximum power transmitted by constant wear and constant
pressure theories; validity of theories
Gear trains: simple, compound and epicycle gear trains; velocity ratios; torque,
speed and power relationships; efficiency; fixing torques
4 Be able to determine the dynamic parameters
of rotating systems
Plane mechanisms: slider crank and four bar linkage mechanisms; production of vector diagrams
and determination of kinetic characteristics
Balancing: single
plane and multiplane rotating mass systems; Dalby’s method for determination
of outofbalance forces and couples and the required balancing masses
Flywheels: angular momentum; kinetic energy;
coefficient of fluctuation of speed; coefficient of fluctuation of
energy; calculation of flywheel mass/dimensions to give required operating
conditions
Effects of coupling: conservation of angular momentum; common final velocity
and energy loss due to coupling of two freely rotating systems
Learning outcomes and assessment criteria

Learning outcomes

Assessment criteria for pass




On successful completion of

The learner can:




this unit a learner will:












LO1 Be able to determine the


1.1

apply the relationship between longitudinal
and



behavioural
characteristics of



transverse strain to determine the
dimensional



materials
subjected to



effects of uniaxial loading on a given
material



complex
loading systems


1.2

determine the effects of twodimensional
and three











dimensional loading on the dimensions of a
given






material





1.3

determine volumetric strain and change in
volume






due to threedimensional loading





1.4

apply the relationship between elastic
constants









LO2 Be able to determine the


2.1

apply the relationship between bending
moment,



behavioural
characteristics of



slope and deflection to determine the
variation of



loaded
beams and cylinders



slope and deflection along a simply
supported beam





2.2

determine the principal stresses that occur
in a thin






walled cylindrical pressure vessel





2.3

determine the distribution of the stresses
that occur






in a pressurised thickwalled cylinder









LO3 Be able to determine the


3.1

determine the dynamic parameters of a belt
drive



dynamic parameters of power


3.2

determine the dynamic parameters of a
friction



transmission system elements







clutch












3.3

determine the holding torque and power
transmitted






through compound and epicyclic gear trains









LO4 Be able to determine the


4.1

determine the parameters of a slidercrank
and a



dynamic
parameters of



fourbar linkage mechanism



rotating
systems


4.2

determine the balancing masses required to
obtain











dynamic equilibrium in a rotating system





4.3

determine the energy storage requirements
of a






flywheel





4.4

determine the dynamic effects of coupling
two freely






rotating systems.








Guidance
Links
This unit
can be linked with Unit 1: Analytical Methods for Engineers, Unit 2:
Engineering Science, Unit 35: Further Analytical Methods for Engineers and
Unit 60: Dynamics of Machines.
Essential requirements
Sufficient
laboratory/test equipment will need to be available to support a range of
practical investigations.
Employer engagement and vocational contexts
Liaison with
employers would prove of benefit to centres, especially if they are able to
offer help with the provision of suitable mechanical systems/equipment that can
be used to demonstrate applications of the principles.
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