Analysis of Mechanism

PPT Designed By:
Mohammed Limdiwala

Contents
 Coupler Curves
 Toggle Position
 Transmission Angle
 Mechanical Advantage
 Acceleration Analysis
 Coriolis Component of acceleration

Coupler Curves
 Def:
 A coupler curve is the locus of a point on the
coupler link.
 For the mechanisms considered, the
displacement of the links joined with the
fixed link was the input or output of the
simple mechanisms.

Coupler Curves
 In great number of applications the output
from a simple mechanism is the path
traced by one of the points on the coupler
link.
 These paths are generally called “coupler
point curves” or “coupler paths”.

Toggle Position
 There are various, methods and synthesis
that could be used to obtain trail solution to
motion control problem.
 One of such rapid process is toggle
position.
 In this technique, one needs to check
whether the mechanism reaches all the
desired position without encountering a
limit position.

Toggle Position
 The toggle positions are determined by the
co-linearity of two of the moving links.
 Hence any mechanism at its limit of motion
is known as Toggle position.

Toggle Position
 Example showing toggle position
technique.

Transmission Angle
 The angle µ between the output link and
the coupler is known as transmission
angle.
 As shown in fig, if link AB is input & the
force applied to output DC is transmitted
through coupler BC.
 For particular value of force, the
torque is max when µ is 90º.

Transmission Angle
 When BC and DC are coincident µ is 0 and
the mechanism would lock.
 When µ deviates a lot from 90º, the torque
on output link decreases.
 Generally µ is kept more than 45º.
 The max and min value of µ can be found
by putting dµ/dθ equal to 0.

Transmission Angle
 It can be seen that µ is max when θ is
180º, & min when θ is 0º.
 But this happens only in double crank or
rocker crank mechanism.
 The max and min value of µ is both
mechanisms are given in next slide.

Mechanical Advantage
 The mechanical advantage (MA) of a
mechanism is the ratio of the output
force/torque to the input force/torque at any
instant.
 In the given fig, is friction and inertia forces
are ignored,
 Input torque T2 is applied to link 2
 Output resisting torque T4 produced at link 4

Mechanical Advantage
 Power input = Power Output
 Or MA = T2 / T4 = ω2 / ω4
 Thus it is reciprocal of velocity ratio.
 But in case of crank-rocker, ω4 is 0, and γ
becomes 180º or 0º, making MA infinity.
 Hence only a small input torque can overcome a
large output torque load.
 Extreme position of linkage points are known as
Toggle points.
T2 ω2 = T4 ω4

Acceleration Analysis
 Acceleration analysis of mechanisms can be
performed vectorially using the relative
acceleration concept, usually starting with the
given values and work through the mechanism by
way of series of points A, B, C, etc.
 important consideration is that the acceleration
analysis cannot be performed without performing
the velocity analysis since the normal and Coriolis
acceleration components can only be determined
after the velocity analysis.

 An Example.

 The triangles abc formed on the velocity and
acceleration polygons are similar to the triangle
ABC of the mechanism link. The sense of abc is
similar to the sense of ABC

 Acceleration of a link in pure rotation.

Coriolis Component of Acc.
 By derivation of the five-term acceleration
equation with a spinning and translating reference
frame, we see that there are two terms that appear
when an object moves inside this rotating frame.
One of these is Coriolis acceleration.
 The Coriolis term is
𝑎⃗ 𝐶𝑜𝑟=2Ω⃗×𝑣⃗ 𝑥𝑦
 Components of Coriolis acceleration involve only
two velocities
 The rotational velocity of the rotating frame,
 the velocity of an object within this rotating frame

 Example a rotating rod with a
collar moving along the rod.
 To understand coriolis
component of acc. Let us take an
example.
 A cockroach is moving on a old Vinyl LP record.

 Let’s consider the simple situation where the
rotational speed Ὠ is constant and the cockroach’s
walking velocity is also constant.
 The following two fig shows position of cockroach
at instant t and t+∆t.

 Coriolis acceleration = 2Vslip
 Coriolis acceleration is normal to the radius, OP,
and it points towards the left of an observer
moving with the slider if rotation is
counterclockwise. If the rotation is clockwise it
points to the right.
 To find the acceleration of a point, P, moving on a
rotating path: Consider a point, P’, that is fixed on
the path and coincides with P at a particular
instant. Find the acceleration of P’, and add the
slip acceleration of P and the Coriolis acceleration
of P.
 AP=acceleration of P’ + acceleration of P seen
from observer moving with rod + Coriolis
acceleration=AP’ + Ap
slip + AP
Coriolis

 Application : Slotted Lever mechanism.

 Relation between accelerations of B2 (on crank)
and B3 (on slider)

Analysis of Mechanism

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Analysis of Mechanism