computer aided design for synthesizing mechanism with...
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Abstract— Transmission angle is the smaller angle between
coupler link and output link of a planar mechanism considered as a
significant criterion of mechanisms design. Transmission angle can
be considered an optimum angle, when its extreme values variations
are equally around 900.
Synthesizing crank rocker mechanism with optimum transmission
angle is the most important and complicated part of mechanism
design, there is a lack of a computerized mechanism design, this
problem motivates to design a fast software to help mechanical
designers. Developed software called (SYNTH-MECH LAB)
created as a fast instantaneous tool for synthesizing crank rocker
mechanism with a desired optimum range of transmission angle
using Visual Basic-6 programming language. The software is helpful
for mechanical designers, engineers and researchers through
providing an instantaneous calculation of suitable mechanism links
ratios for a definite synthesized transmission angle range. Also, the
software affords an attractive animation of the synthesized
mechanism simultaneously with linkages ratios calculations.
Keywords—Computer Aided Design, Transmission Angle,
Mechanism Synthesis, Design Technique.
I. INTRODUCTION
RANSMISSION angle can be defined as the smaller angle
between the direction of absolute velocity vector of rocker
link and direction of velocity difference vector of driving link
at the connection joint as in [1]. Reasonable optimal
transmission angle can treat the most mechanical problems in
mechanisms as in [2]. Restricting transmission angle range to
be bounded by a two specific limits can make transmission
angle's optimizing problem easier [3]. Obviously, the
maximum and minimum transmission angles are highly
depending on the rocker angle. Furthermore, the acceptable
deviation of the transmission angle value from 90o can
guarantee a smooth motion without undesirable vibrations at
high speed [4].
On the other hand, a wide transmission angle range plays
an effective role in reducing the effectiveness of force
transmission where noise and jerk appear at high speed of
mechanism motion [5].
An analytical synthesis of mechanism motion between two
small separated positions considering the minimum and
maximum transmission angles is presented in [6].
Khaled M. Khader is member of the teaching staff with the Department of
Production Engineering & Mechanical Design, Faculty of Engineering,
University of Menoufia, Shebin El-kom, Menoufia, Egypt. (corresponding
author's phone: 00201223538574 ; fax 0020482235695;e-mail:
khkhm62@hotmail.com).
Also, analytical optimization of four bar transmission angle
is presented in [7] as a solved example through supposing the
dimension of coupler link in addition to dimensions ranges of
fixed, crank and rocker links. A new method of designing
four bar function generators with optimum angle when their
extreme values have variations are equally around 90o is
presented in [8]. Also, some different transmission angle
ranges as 35o-145o; 45o-135o are suggested in [4]. Many
researches are dealing with the advantages of using computer
aided design (CAD) of mechanisms as [9] which describe
some examples to show current trends in the field of linkage
design and discuss future strategies of CAD. As well as,
designing planar mechanisms dealing with CAD are
presented in [10],[11]. Also, the development of computer
aided industrial design technology discussed in [12]. An
analytical method is presented in [13] using computer
programming for determining the values of velocity and
acceleration of coupler and rocker links at different positions
of the crank link. Optimal kinematic synthesis using CAD for
planar crank rocker mechanisms for a specific time ratio and
stroke presented in [14].
A master thesis [15] were synthesized a planar mechanism
for three multiply separated positions using CAD. Also,
another master thesis [16] is dealing with synthesizing planar
mechanisms with straight line coupler curves. Many
researches are dealing with CAD as designing spherical
mechanism using CAD software in [17] for designing and
modeling new magnetic sealing mechanism is presented in
[18], while, [19] also, presented a computer aided position
analysis and modelling of crank and slotted lever mechanism.
Development of surface micro-machined mechanisms is
presented using CAD in [20]. As well as, designing of a
special clamping mechanism is introduced using CAD in
[21].
A software for designing of multi-stage gearboxes
presented in [22] written in Visual Basic language with an
easy interface menus in order to quickly help the designers.
This paper trying to present an easy and fast designing tool
in software form called (SYNTH-MECH LAB) has codes in
Visual Basic language which is created for synthesizing crank
rocker mechanism with the desired optimum range of
transmission angle for helping the mechanical designers.
SYNTH-MECH LAB provides the designers with an
instantaneous calculations of suitable mechanism links ratios
for a definite synthesized transmission angle range. As well
as, this software affords an attractive animation of the
synthesized mechanism simultaneously with linkages ratios
calculation.
Computer Aided Design for Synthesizing
Mechanism With Optimal Transmission Angle
Dr. Khaled M. Khader
T
6th International Conference on Trends in Mechanical and Industrial Engineering (ICTMIE'2015) Sept. 13-14, 2015 Dubai (UAE)
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II. OPTIMUM TRANSMISSION ANGLE
The transmission angle (μ) of a planar mechanism is
indicated in Fig. 1 as follows;
Fig. 1 Transmission Angle μ
Where; fixed, crank, coupler and rocker links lengths are L1,
L2, L3 and L4, respectively. The transmission angle ( μ ) of the
four bar planar mechanism can be formulated as follows;
43
2122
21
24
231
2
cos2cos
LL
LLLLLL
(1)
Maximum transmission angle (μmax) and the minimum
transmission angle (μmin) of a crank rocker mechanism is
shown in Fig. 2 as follows;
Fig. 2 Orientation of Maximum and Minimum Transmission Angle
The minimum value of transmission angle (μmin) occurs at
0o of crank angle while maximum value of transmission angle
(μmax) occurs at 180o of crank angle as in [23]. Therefore, μmin
and μmax can be written as in [23], [24] as follows;
43
21
43
22
21
24
23
maxmin,2
cosLL
LL
LL
LLLL
(2)
Obviously, optimal transmission angle occurs when this
angle has maximum and minimum values which have equally
variations around 90o as in [8]. The nomograms of optimal
transmission angle using the meaning of {μmin=(π/2)-δ and
μmax=(π/2)+δ} are presented in [25]. Where, the value of the
angle (δ) can be assumed related to the crank rocker
mechanism's designer requirements for calculating the
synthesized mechanism linkages ratios (R2, R3 and R4). These
ratios can be written as follows;
144133122 /Rand/R,/R LLLLLL
(3)
The nomogrames in [25] are depending on assuming only
two values, the first assumed value is the desired rocker angle
(ϕI) which corresponds to the minimum transmission angle
and the second one is the desired transmission angle range
through supposing the value of (δ), where, the synthesized
mechanism linkage ratio (R2) can be written as follows;
1
12
1R2
M
M
M
M
(4)
Where, (M) is; 2
min
minI
2
min
I
sin
)(sin
sin
sin
M
(5)
Also, the synthesized mechanism linkage ratio (R3) can be
written as follows;
)R1)(sin
sin(R 2
min
I3
(6)
As well as, the synthesized mechanism linkage ratio (R4) can
be written as follows;
)R1(sin
)(sinR 2
min
minI4
(7)
Clearly, the pervious three ratios R2, R3 and R4 are only
functions of (ϕI) and (δ).
Hence, the software called (SYNTH-MECH LAB) which is
presented in this paper can directly synthesizing crank rocker
mechanism through substituting the two values (ϕI and δ)
which selected by software's user in (4), (6) and (7).
Thus, (SYNTH-MECH LAB) can directly synthesizing
crank rocker mechanism using the desired selected value of
angle (ϕI) and the value of angle (δ) which leads to
calculating two angles (μmin and μmax). The presented software
(SYNTH-MECH LAB) affords an instantaneous animation of
the synthesized mechanism meanwhile calculating the
synthesized linkages ratios.
Satisfying the condition (μmin +μmax = π) for crank rocker
mechanism leads to time ratio equal one as in [25], [26]
which improves its dynamic characteristics.
III. CRANK ROCKER MECHANISM'S MOTION ANALYSIS
The rocker link (L4) which is indicated in Fig. (3) has two
extreme positions of its oscillating motion through the crank
angle (00≤ψ≤3600) with satisfying linkages lengths constrains
regarding to these two extreme positions as follows;
6th International Conference on Trends in Mechanical and Industrial Engineering (ICTMIE'2015) Sept. 13-14, 2015 Dubai (UAE)
13
0
0
0
0
0
0
2143
3421
4321
3241
4231
1432
LLLL
LLLL
LLLL
LLLL
LLLL
LLLL
(8)
Regarding to Fig. 3, the angle (ɵ3) of the coupler link can
be calculated as;
)2()(where,
)(where,
1124
11423
(9)
Fig. 3 Crank Rocker Mechanism Geometry
Also, the angle (ϕ) of the rocker link can be calculated as
follows;
)2()(where,
)(where,
11311
11311
(10)
Where, (ɵ1) is the angle of the fixed link (L1), the length (L)
in addition to angles (φ1, φ2, φ3, φ4 & μ) can be written as
follows;
43
224
231
3
24
2231
4
4
23
2241
3
2
21
2221
2
1
22
2211
1
2122
21
2cos
2cos
2cos
2cos
2cos
cos2
LL
LLL
LL
LLL
LL
LLL
LL
LLL
LL
LLL
LLLLL
(11)
Clearly, rocker angular velocity ( ϕ' ) and rocker angular
acceleration ( ϕ" ) are important factors of mechanism. Thus,
rocker angular velocity (ϕ') and the rocker angular
acceleration ( ϕ" ) can be found by derivation of (10).
IV. SYNTH-MECH LAB SOFTWARE
The developed software called (SYNTH-MECH LAB)
directly synthesizes crank rocker mechanism using the
desired selected value of angle (δ) leading to calculating two
angles (μmin and μmax) in addition to value of rocker angle (ϕI)
corresponds to the desired minimum transmission angle
(μmin).
A. Software Welcome Menu:
The software welcome menu is indicated in Fig. 4. This
menu includes two buttons. The first button allows the
software's user for synthesizing the crank rocker mechanism
with desired optimal transmission angle range. While, the
second button allows the software's user for selecting any
lengths of crank rocker mechanism linkages and showing the
mechanism positions parameters in addition to showing its
motion.
Fig. 4 Welcome menu of SYNTH-MECH LAB software
B. Software Menu of Mechanism's Synthesis:
The flow chart of the first part of SYNTH-MECH LAB
software of mechanism's synthesis is indicated in Fig. 5 as
follows;
6th International Conference on Trends in Mechanical and Industrial Engineering (ICTMIE'2015) Sept. 13-14, 2015 Dubai (UAE)
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Fig. 5 Flow chart of first part of SYNTH-MECH LAB software
The software menu of mechanism's synthesis is indicated
in Fig. 6. This menu provides software's user with an
attractive interface for allowing him to directly select the
desired vales of (δ) and (ϕI) using an easy scroll bars as
indicated in Fig. 7.
Fig. 6 Software menu of mechanism's synthesis
Fig. 7 Scroll bars for selecting desired values
C. Menu of Mechanism's Positions Analysis and its Motion:
Fig. 8 shows the flow chart of second part of SYNTH-
MECH LAB software of mechanism's positions analysis and
its motion.
The menu of the second part of the developed software is
indicated in Fig. 9 which provides software's user with an
attractive interface for allowing him to directly select the
desired crank rocker mechanism linkages lengths (L1, L2, L3
and L4) and the crank angle (ψ) in addition to fixed link angle
(ɵ1).
The menu which is presented in Fig. 9 includes button
("Press to draw cycle") for showing attractive animation for a
complete turn of the crank. As well as, another buttons are
included for presenting the rocker angle (ϕ), the coupler
angle (ɵ3), the transmission angle (μ), the rocker angular
velocity ( ϕ' ), the coupler angular velocity (ɵ'3), the rocker
angular acceleration ( ϕ" ) and the coupler angular
acceleration (ɵ''3) through a complete turn of the crank as
shown in Fig. 10.
6th International Conference on Trends in Mechanical and Industrial Engineering (ICTMIE'2015) Sept. 13-14, 2015 Dubai (UAE)
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Fig. 8 Flow chart of second part of SYNTH-MECH LAB software
Fig. 9 Menu of mechanism's positions analysis and its motion
Fig. 10 Graphs of SYNTH-MECH LAB software
V. RESULTS
Using the developed software menus, the software's user
can select value of angle (δ) which leads to calculate the two
angles (μmin and μmax) in addition to selecting value of angle
(ϕI) of the rocker angle which corresponds to the desired
minimum transmission angle (μmin) as follows; ϕI =1000 and
δ=350 which leads to the values μmin=550 and μmax=1250. The
corresponding calculated values (L1, L2, L3 and L4) are;
L1=100 units, L2=29.5 units, L3=84.7 units and L4=60.8
units. The transmission angle (μ) and the rocker angle (ϕ) can
be calculated also using (1), (10) and (11) for each crank
angle (ψ). The relation between (ψ) and both (μ & ϕ) is
shown in Fig. 11 as follows;
Fig. 11 Relation between (ψ) and both (μ & ϕ)
VI. CONCLUSION
The developed software which presented in this paper called
(SYNTH-MECH LAB) created as a fast instantaneous tool for
synthesizing crank rocker mechanism with a desired optimum
range of transmission angle. The software is helpful for
mechanical designers and researchers through providing
them with an instantaneous calculations of suitable
mechanism links ratios for a definite synthesized
transmission angle range. Also, the software affords an
attractive animation of synthesized mechanism
simultaneously with linkages ratios calculation.
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6th International Conference on Trends in Mechanical and Industrial Engineering (ICTMIE'2015) Sept. 13-14, 2015 Dubai (UAE)
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6th International Conference on Trends in Mechanical and Industrial Engineering (ICTMIE'2015) Sept. 13-14, 2015 Dubai (UAE)
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