FOUNDATION of MECHANICS 1MECHANICS of MACHINES
MECHANISM & MACHINE SCIENCE
The Mechanics of Machines deals with problems associated with themovement and equilibrium of mechanical systems. The M.o.M. main topics are:movement and equilibrium of mechanical systems. The M.o.M. main topics are:
• Composition of the machines: degrees of freedom of a mechanism, mechanical efficiency ;mechanical efficiency...;
• Tribology: contact between the organs of the machines during their relative motion, power transmission, friction, energy dissipation, wear, rolling friction, lubrication...;
• Theory of mechanisms: machine behavior from the functional viewpoint; linkages couplings cams gears and gearing brakeslinkages, couplings, cams, gears and gearing, brakes...
• Dynamics: calculation and balancing of inertia actions, coupling between actuator and operating machine, functioning of machines and plants in p g g psteady states or for transients…
MACHINE
• Mechanical system that transmits and transforms force and motion (i ) t f ifi t k(i.e. energy) to perform a specific task:
– MECHANISM (speed reducers and variators, belt/chain transmissions, cam mechanisms coupler )cam mechanisms, coupler...)
– MOTOR (IC engines, electric motors, hydraulic motors...)– GENERATOR (pumps and compressors, dynamos, turbines...)– OPERATING (or WORKING) MACHINE (machine tools, automatic m.,
packaging m., farming m., textile m., lifting and transport m., vehicles, robots...)
p mp
speed reducers
pump
IC engine industrial robot
MODELLING
• Starting point: defining a proper model of the examined h i l t id i ll th tmechanical system, considering all the aspects we are
interested in (and only those) and assuming reasonable hypotheses and approximationshypotheses and approximations.
REAL SYSTEM
PHYSICAL MODEL
MATHEMATICAL MODEL
SOLUTION:
analytical
numerical
graphical
MODELLING
crankshaft
Slider-crank mechanism
piston
conrod
accessories
ANALYSES
• Three kinds of analysis in Mechanics of Machines:
• Kinematic analysis (+ Kinematic synthesis)
• Static analysis
• Dynamic analysis– Kinetostatic
(Inverse dynamic)
– Dynamic(Direct dynamic)
COMPOSITION OF MECHANISMSbasic definitions
Rigid body: solid body in which the distance between any two g y y ygiven points is constant.
A basic concept in Kinematics is the Degree of Freedom (DOF)
Number of independent kinematic variablesrequired to completely define the configurationof a system at any instant of timeof a system at any instant of time.
• DOFs of a free rigid body in a 2D Space (plane):
DOF f f i id b d i 3D S
3
6• DOFs of a free rigid body in a 3D Space: 6
COMPOSITION OF MECHANISMSbasic definitions
• Link
• Kinematic element & Kinematic joint (or pair)• Kinematic element & Kinematic joint (or pair)
• Mechanism: system of bodies designed to convert
motion of
for one or several bodies intoforces on
constrained motion of
forces onor other bodies.forces on
COMPOSITION OF MECHANISMS
COMPOSITION OF MECHANISMSbasic definitions
• Link
• Kinematic element & Kinematic joint (or pair)• Kinematic element & Kinematic joint (or pair)• rigid vs. flexible joints
• contact surface vs. contact point/segment joints
- Lower pair: rigid AND contact surfacep g
- Higher pair: non rigid OR point/segment contact
l h i l i j i t• planar vs. spherical vs. generic joints
• linkage: planar mechanism with lower joints only
KINEMATIC JOINTS
REVOLUTE
PRISMATIC
HELICAL
KINEMATIC JOINTS
CYLINDRICAL RevolutePLANAR HIGHER PAIRPLANAR HIGHER PAIR
PLANE on PLANEPLANE on PLANE
SPHERICAL
KINEMATIC JOINTS
Relative motion 2-1
Rolling ( 21) 0tMV
g( 21) 0nMV
Projections of the kinematic Sliding(Rolling possible as well)( 21) 0MV
( 21) 0tMV
• Projections of the kinematic elements in the plane: common tangent line in M
(Rolling possible as well)( 21) 0nMV
V
• Contact kept during the relative motion CONJUGATE PROFILES
Impact or Separation( 21) 0nMV
( 21) tMV
CONJUGATE PROFILES
KINEMATIC JOINTS
DOF Class Conventional name Rotation Translation Helical motion
1 C1
R (Revolute)P (Prismatic)H (Helical)
11
1
2 C2
RTC (Cylindrical)CS (Planar higher pair)R
2111
11
1R 1 1
3 C3
S (Spherical)SASL
322
11SL
PP (Plane on plane) 1 2
4 C4
SCSE
33
114 E
CC 2 2
5 C5 S5 3 2
Bold: most used joints Red: planar joints Highlighted: lower pair
COMPOSITION OF MECHANISMS
Kinematic chain vs. MechanismNo link is fixed a priori
One link is chosen as
basic definitions
fixed a priori chosen as the frame
Kinematic chains (examples)
STEPHENSON WATTSTEPHENSON kinematic chain
WATT kinematic chain
Mechanisms (from previous kin. ch.)
DOFs of MECHANISMS
Calculating the DOFs of a mechanism: the Grübler’s formula g(DOF := Number of independent kinematic variables required to
completely define the configuration of a system at any instant of time)
m = number of linksc = number of joints
[1 link is the frame][(6 i) DOFs are constrained]ci = number of joints
leaving i DOFs free[(6 – i) DOFs are constrained]
1 2 3 4 56 ( 1) 5 4 3 2l m c c c c c 3D)
3( 1) 2l m c c2D) 1 23( 1) 2l m c c 2D)
DOFs of MECHANISMS
Calculating the DOFs of a mechanism: the Grübler’s formula g
b f li kNJ = number of jointsl = mechanism DOFsl DOF l ft f b th i th j i t
JN
m = number of links li = DOFs left free by the i-th joint
16 ( 1) (6 )i
il m l
3D)
3( 1) (3 )JN
il m l 2D)1i
l number of configuration variables to be actuatedb f h d i / h iby means of motors or other devices/mechanisms
DOFs of MECHANISMS
Examplesp
Crank–slider mechanism Four-bar linkage
l = 1 l = 1
Four bar linkage
l = 1 l = 1
Cam systemBelt & Pulleys transmission
CAM SYSTEMS: overview
DOFs of MECHANISMS
Examplesp
l = 3 l = 3
l = 6 l = 6l = 6 l = 6
DOFs of MECHANISMS
Examplesp
l = 2
DOFs of MECHANISMS
Caution in using Grubler’s formula!g
• 3D vs. 2D SpacesR
A1
AM = MB
5R
RB
23
4
MR
R
• Redundant constraints
B4R R
• Ineffective/meaningless constraints 2
4
3 1
6( 1) 5 4 3 2l m c c c c c1 23( 1) 2l m c c
41 2 3 4 56 ( 1) 5 4 3 2l m c c c c c
DOFs of MECHANISMS
Ineffective/meaningless constraintsIneffective/meaningless constraints
McPherson SuspensionMcPherson Suspension