International Journal of Engineering Trends and Technology (IJETT) – Volume 32 Number 3- February 2016
Study of Paucellier Mechanism
Dr. Ali Hasan
Mechanical Engineering Department,
Jamia Millia Islamia, New Delhi.
Abstract –in this paper, the author presented the
geometry point A moves in a circular path and as the
design procedure of shaper mechanism using
point A moves in a circle point P traverses an exact
Peaucellier
linkage.
The
been
straight line path normal to the line joining O2 and
formulated
between
the
angles
O4. From the construction of the Peaucellier linkage
subtended by the linkages in the Paucellier
it is clear that this is a much more complex
Mechanism during its motion in shaper mechanism.
mechanism
The stroke length has been calculated and a
generating approximate straight lines, which were
relationship has been shown among different
simple four bar linkages. This mechanism has eight
variables. a prototype also has been tested.
members and six joints.
relation
lengths
has
and
than
the
mechanisms
1) Key Words- mechanism, height of mechanism
and stroke length
2) Introduction:
The Paucellier linkage was invented in 1864.It is
named after Charles-Nicolas Paucellier (1832–1913),
a French army officer. It was the first planar linkage
capable
of
transforming
perfect straight-line
motion,
rotary
and
motion
vice
into
versa.
Paucellier mechanism is one of the exact straight
line motion mechanism .It works on lower pair
linkages implying eight links rhomboidal system in
such a way so as to produce straight line motion at
its output. Paucellier mechanism can convert an
input circular motion to the exact straight line
motion. The construction of this mechanism is such
Design Procedure A Mathematical model of paucellier mechanism is
shown in Figure 2.
that the point which is connected to the crank moves
in a circular path and the point traversing the straight
line is selected as the output point. The linkage has a
rhombic loop formed of the equal length members, 5,
6, 7 and 8 as shown in Figure 1. Two equal length
links are connected to the opposite corners of the
rhombus at one end and to a common fixed point at
the other ends. The point A of the rhombus is
connected to a fixed point O2 through the link 2.
The length of the link 2 is equal to the distance
Mathematical model of paucellier mechanism
between points O2 and O4. By the constraints of the
ISSN: 2231-5381
http://www.ijettjournal.org
Page 132
International Journal of Engineering Trends and Technology (IJETT) – Volume 32 Number 3- February 2016
(i).It consists of 8 links i.e. a fixed link OO1 and the
straight links O1A, OC, OD, AD, DB, BC and CA
are connected by turning pairs.
(ii)The pin at A is constrained to move along the
circumference of a circle.
(iii) AC = CB = BD = DA; OC = OD; and OO1 =
O1A
(iv)From the triangles ORC and BRC,
(v)Therefore the product OB X OA remains constant.
Hence the point B traces a straight path
perpendicular to the diameter OP.
(OC)2 = (OR)2 + (RC)2 ------------------------------(1)
and
(BC)2 = (RB)2 + (RC)2 --------------------------------(2)
Subtracting equation (2)from (1), we get
(OC)2 - (BC)2 = (OR)2 - (RB)2 = (OR+OB) (OROB) = OB X OA
Assumptions:- (i) Values of w and h are to be
assumed. (ii) l = (h/3) , (iii) d = 2w
Here, w is the width of the bar, l is the horizontal
length of the mechanism, h is the vertical height of
the mechanism, r is the length of the crank bar, lb is
the length of each bar of rhomboidal system, lr is the
length of rod joining bars of rhomboidal system to
the fixed point, d is the vertical height of the
rhomboidal system, 2θ is the angle subtended
between the rods joining bars of rhomboidal system
to the fixed point, See Figure 3 and Figure 4.
2r = h-d
In ∆ABD, Tan θ = (AD/BD) ,Tan θ =
{(l/2)/h} , or Ɵ= Tan-1{(l/2)/h}
In ∆BHF, HB = 2r + (d/2), Tan θ =
(FH/HB) or FH = HB × Tan θ
FH = {2r + (d/2)} Tan θ
In ∆FHE, HE = d/2 ,Tan α = (HE/ FH) , or
Tan α = {(d/2) / (2r + (d/2)) Tan θ}
Sin α = (HE/FE) , or FE = (HE/ Sin α) ,
{FE = lb., HE = (d/2)}
lb. = {(d/2)/ Sin α}
Sin θ = (FH/FB) or Sin θ = {(2r + (d/2))
Tan θ/ lr}
lr = {(2r + (d/2)) Tan θ/ Sin θ} or lr = {(2r
+ (d/2))/ Cos θ}
(L/2) = h Tan γ or L = 2h Tan γ.
Results: Results are shown in Table-1,2 and 3.
ISSN: 2231-5381
http://www.ijettjournal.org
Page 133
International Journal of Engineering Trends and Technology (IJETT) – Volume 32 Number 3- February 2016
CASE 2:- h is kept constant and Wmin is varied
h= 1200 mm
Contants:- h, wmax , d ,θ, lb , lr .
Variables:- W‟, Ф, β ,ls ,γ ,L .
Quantity on which effect to be noted:- L
h= 1200 mm constant , W= 150 mm.
CONCLUSION
This paper is about formulating the relations
between the lengths and angles subtended by the
linkages of a paucellier mechanism. The main aim of
this paper is to provide a design procedure for the
advancement of a shaper mechanism so as to
minimizing the errors during manufacturing and
working of the mechanism and to avoid the hit and
trial method for determining the various lengths and
angles of the mechanism. In this paper few relations
are deduced to calculate the working angle and by
knowing the working angle, one can easily program
the motor power to op
ISSN: 2231-5381
http://www.ijettjournal.org
Page 134
International Journal of Engineering Trends and Technology (IJETT) – Volume 32 Number 3- February 2016
References
1.[Erdman and Sandor, 1988] Erdman A. G. and Sandor G. N.,
“Advanced Mechanism Design”, Vol. I and II, Prentice Hall of
India.
2.[Ghosh and Mallik, 1988] Amitabha Ghosh and Ashok Kumar
Mallik, “Theory of Mechanisms and Machines”, East – West
Press Pvt. Ltd., New Delhi, pp. II Edition.
3. [Hain, 1967] Kurt Hain, “Applied Kinematics” McGraw-Hill,
New York,1967.
4.[Hartenberg and Denavit, 1964] Hartenberg S. and Denavit J.,
“Kinematic Synthesis of Linkages” McGraw-Hill, New York,
1964.
5..[Hasan A.,2009] “ Identification of Isomorphism among
Kinematic Chains and Inversions Using Link Adjacency
Values”,International J. of Mech. and Materials Engineering
(IJMME), No.3, Vol. 4, 309-315.
6.[Hasan A.,2010] “ Application of Link Adjacency Values to
Detect Isomorphism among Kinematic Chains”,Int. J. Mech.
Mater. Design, ”, 6,157-162.
8.[Hasan A., 2007]“ Systematic Development of Kinematic
Chains and Mechanisms from a given Assortment of
Links” ”,Journal of „Institution of Engineers (India), Vol. 88,1519.
9.[Hasan A., 2007]“ Isomorphism in Kinematic Chains Using
Path Matrix”,Journal of Institution of Professional Engineers
(IPENZ), 1-8.
10.[Hasan A.,2009] “ Isomorphism and Inversions of Kinematic
Chains up to 10 Links ”,Journal of „Institution of Engineers
(India), Vol. 90, 10-14.
11. [Mohd,1998] Mohd A. “Kinematic chains structural
modelling and correlation with machine performance”, M.Tech.
Dissertation, IIT Delhi.
12.[Preben W. Jensen, 1991] Preben W. Jensen, “Classical and
Modern Mechanism for Engineers and Inventors Marcel Decker,
Inc, New York .
15. [Mohammad Javed, Dr.Parul Gupta, and Dr.Vishal
Saxena,2015, “Role of Service Quality and Customer Satisfaction
in Four Wheeler Automobile Service Industry: A Review”,
International Journal of Engineering Trends and Technology ,
Volume-28 Number-6,pp.288-290.
7.[Hasan A.,2010] “ Isomorphism Identification of Compound
Kinematic Chain and Their Mechanism”,i-manager‟s Journal on
Mechanical Engineering, Vol. 2 , No. 1, 7-15.
ISSN: 2231-5381
http://www.ijettjournal.org
Page 135