Computer Aided Design for Synthesizing Mechanism With ...psrcentre.org/images/extraimages/915018.pdf · angle is the most important and complicated part of mechanism design ... using

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:

[email protected]).

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)

12

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;


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;


14

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.


15

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.

REFERENCES

[1] R. Hartenberg and J. Denavit, in: Kinematic Synthesis of Linkages,

McGraw-Hill, New York, 1964, pp. 46-47.

[2] S. Balli and S. Chand, ―Transmission Angle in Mechanisms-Triangle in

Mech.‖, Mechanism and Machine Theory, vol. 37, no. 2, pp. 175-195,

2002.

[3] R. Soylu, ―Analytical Synthesis of Mechanisms – Part-1‖, Mechanism and

Machine Theory, vol. 28, no. 6, pp. 825-833, 1993.

[4] P. Eschenbach and D. Tesar, ―Link Length Bounds on the Four Bar

Chain‖, Journal of Engineering for Industry Trans. ASME, vol. 93, no. 1,

pp. 287-293, 1971.

[5] D. Tao, in: Applied Linkage Synthesis, Addison-Wesley, Reading, MA,

1964, pp. 7-12.

[6] P. Rao, ―Kinematic Synthesis of Variable Crank-rocker and Drag linkage

planar type Five-Bar Mechanisms with Transmission Angle Control‖,


16

International Journal of Engineering Research and Application, vol. 3,

no. 1, pp. 1246-1257, 2013.

[7] S. Jian, ―Analysis and Optimization of the Transmission Angle of Crank

Rocker Mechanism‖, in International Conference in Mechatronic,

Electronic, Industrial and Control Engineering MEIC, Shenyang, China,

April 2015, pp.155-158.

[8] K. Gupta, ―Design of Four-Bar Function Generators with Mini-Max

Transmission Angle‖, Journal of Engineering for Industry Trans. ASME,

vol. 99, no. 2, pp. 360-366, 1977.

[9] A. Erdman, ―Computer-Aided Mechanism Design: Now and the Future‖,

Journal of Mechanical Design, vol. 117, no. B, pp. 93-100, 1995.

[10] L. Yang, Y. Lu, N. Ye and L. Yuan, ―High-Order Dimension Synthesis of

Planar/Spatial Mechanisms with One-DoF by CAD Vibrational

Geometry‖, Journal of Modelling and Simulation in Engineering,

Hindawi Publishing Corporation, vol. 2012, pp. 1-9, 2012.

[11] B. Chandrakar and M. Soni, ―Design and Optimization of Slider and

Crank Mechanism with Multibody Systems‖, International Journal of

Science and Research, vol. 4, no. 6, pp. 1709-1712, 2015.

[12] M. Yao, ―Discuss the Development of Computer-Aided Industrial Design

Technology‖, International Journal of Computer Science Issues, vol. 10,

no. 1, pp. 188-193, 2013.

[13] N. Yao Alvi, S. Deshmukh and R.Wayzode, ―Computer Aided Analysis of

Four bar Chain Mechanism‖, International Journal of Engineering

Research and Applications, vol. 2, no. 3, pp. 286-290, 2012.

[14] G. Hassaan, M. Al-Gamil and M. Lashin, ―Optimal Kinematic Synthesis

of 4-Bar Planar Crank-Rocker Mechanisms for a Specific Stroke and Time

Ratio‖, International Journal of Mechanical and Production

Engineering Research and Development, vol. 3, no. 2, pp. 87-98, 2013.

[15] E. Demir, Kinematic Design of Mechanisms in a Computer Aided Design

Environment, Master Thesis, Middle East Technical University, Turkey,

May 2005, pp.28-34.

[16] A. Natesan, Kinematic Analysis and Synthesis of Four-Bar Mechanisms

for Straight Line Coupler Curves, Master Thesis, Rochester Institute of

Technology, Collage of Engineering, USA, May 1994, pp.15-23.

[17] J. Ketchel and P. Larochelle, ―Sphinx Cam: Computer-Aided

Manufacturing for Spherical Mechanisms‖, In: Proceedings of DETC’98,

1998 ASME Design Engineering Technical Conferences, Atlanta,

Georgia, USA, September 1998, pp.1-8.

[18] J. Li, ―Computer Aided Modeling and Deign of a New Magnetic Sealing

Mechanism in Engineering Applications‖, Journal of Scientific Research

in Engineering, http://www.scirp.org/journal/eng, vol. 2, no. 1, pp. 41-

46, 2010.

[19] S. Shelare, P. Thakare and C. Handa, ―Computer Aided Modelling And

Position Analysis of Crank And Slotted Lever Mechanism‖, International

Journal Of Scientific and Technology Research, vol. 1, no. 5, pp. 7-10,

2012.

[20] M. Kilani, ―Computer Aided Design Tools in the Development of Surface

Micro-machined Mechanism‖, Jordan Journal of Mechanical and

Industrial Engineering, vol. 5, no. 2, pp. 167-176, 2011.

[21] C. Gorge, ―Computer Aided Design of Clamping Mechanism with

Articulated Arms‖, Journal of Engineering Annals Faculty of

Engineering Hunedoara, pp. 157-161, 2007.

[22] M. Nasser, F. Gomaa, M. Asy and A. Deabs, ―Computer Aided Design of

Multi-Stage Gearboxes‖, International Journal of Advanced Engineering

And Global Technology, vol. 2, no. 12, pp. 148-157, 2014.

[23] T. Patal, ―Synthesis of Four Bar Mechanism for Polynomial Function

Generation by Complex Algebra”, in National Conference in Recent

Trends in Engineering & Technology, B.V.M Engineering Collage,

Nagar Gujarat INDIA, May 2011, pp. 1-5.

[24] S. Matekar, and G. Gogate, ―Optimum Synthesis of Path Generating Four-

Bar Mechanism Using Differential Evaluation and Modified Error

Function‖, Mechanism and Machine Theory, vol. 52, pp. 158-179, 2012.

[25] K. Khader, ―Nomograms for Synthesizing Crank Rocker Mechanism With

a Desired Optimum Range of Transmission Angle‖, (Accepted for

publication) International Journal of Mining, Metallurgy and

Mechanical Engineering to be published, 2015.

[26] P. Roth and F. Ferudenstain, ―Synthesis of a Four Bar Link Path

Generating Mechanisms with Optimum Transmission Characteristics‖, in

Transaction of Seventh Conference of Mechanism, Purdue University,

Lafayette, Indiana, USA, pp. 44-48, 1962.


17

Documents

Computer Aided Design for Synthesizing Mechanism With ...psrcentre.org/images/extraimages/915018.pdf · angle is the most important and complicated part of mechanism design ... using