## The Dynamic Analysis of Cam Mechanism

**Ingrid Delyová**^{1,}, **Darina Hroncová**^{1}, **Peter Sivák**^{1}, **Martin Beliško**^{1}

^{1}Department of Applied Mechanics and Mechatronics, Faculty of Mechanical Engineering Technical University of Košice, Slovakia

### Abstract

This article deals with the dynamic analysis of cam mechanism using MSC Adams. In the first part of this paper is solving the dynamic analysis by using the method of reducing weight and forces value on a moving member of the lifter. The mathematical model of the lifter was designed by using this method of dynamic analysis. The second part deals with the dynamic analysis in the program MSC Adams. The dynamic analysis is important in terms usability of cam mechanism, because of not every shape and characteristics of that cam meets the specific mechanism.

### At a glance: Figures

**Keywords:** cam mechanism, dynamic analysis, velocity, acceleration

*American Journal of Mechanical Engineering*, 2013 1 (7),
pp 266-270.

DOI: 10.12691/ajme-1-7-23

Received October 10, 2013; Revised October 20, 2013; Accepted November 21, 2013

**Copyright**© 2013 Science and Education Publishing. All Rights Reserved.

### Cite this article:

- Delyová, Ingrid, et al. "The Dynamic Analysis of Cam Mechanism."
*American Journal of Mechanical Engineering*1.7 (2013): 266-270.

- Delyová, I. , Hroncová, D. , Sivák, P. , & Beliško, M. (2013). The Dynamic Analysis of Cam Mechanism.
*American Journal of Mechanical Engineering*,*1*(7), 266-270.

- Delyová, Ingrid, Darina Hroncová, Peter Sivák, and Martin Beliško. "The Dynamic Analysis of Cam Mechanism."
*American Journal of Mechanical Engineering*1, no. 7 (2013): 266-270.

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### 1. Introduction

The continuous improvement of automotive industry or general engineering was associated with continuous improvements of mechanisms which generating functional units of drive motor for instance. In this evolution the mechanisms which uses circular or non-circular cams was not any exception neither. The cam mechanisms have been used for a long time until today and are included as an integral part of combustion engines. They are encountered in installations where comes transformation of rotary movement to movement of shifting in practice. The advantage of cam mechanisms is their simplicity and high functionality. The dynamic analysis of the mechanism with a circular cam is the aim of this work. This analysis is necessary when dealing with design of a cam mechanism it to achieve the best result which means to achieve desired properties when is used the smallest amount of material, for instance.

Model of the mathematical cam was developed by using methods of analytical dynamics. In the second part of the dynamic analysis and sizing dimensions mechanism is solution solved by program MSC Adams. Programs such as MSC Adams can facilitate dynamic analysis of various complex mechanisms which simplify and velocity up the analysis results. To the desired results solutions leads correctly preparation of dimensional model in a computer program simulation of MSC. That program allows you to evaluate the results in graphical and numerical form. It can determine kinematics quantities such as: distance, velocity, acceleration, and other physical quantities. The dynamic analysis is important in terms usability of the cam mechanism, because of not every shape and the characteristics of that cam meets the specific mechanism.

### 2. Creation of Movement Equation of Cam Mechanism

By the method of reducing weight and power values on a moving member which is lifter, were created movement equation of cam mechanism shown in the Figure 1. This is not only one method of analysis of dynamics which is so difficult; there are also others where solution of movement equation of cam mechanism is not so easy and demanding. Therefore, the use of the program MSC Adams is very advantageous. In view of the above-mentioned difficulty solving the equations of motion prepared by the method of reducing power and weight values applied to a member of lifting cam mechanism. Due to the transformation from movement of drive member to the driven rotary member with a sliding motion is interesting precisely movement of lifter. The driving torque *M*_{2} is driven with a circular cam mechanism with a flat lifter. Lifting device is pressed against to cam with spring of stiffness *k *and there operates force external *F*. The considering of known geometric - weight variables: *e*, *r*, *h*, *f*_{0}, *I*_{2A}, *m*_{2}, *m*_{3}, *M*_{2}, *k*,* F*, *α*, ^{[6]}.

The dynamic equation of motion of the reduced system onto moved member of the executing motion is defined by *m*_{red}.*a*=*F*_{red} ^{[1, 2]}. It is obvious that we need to derived *m*_{red} and* F*_{red}. In our case where we are looking for the equation of motion member 3 by reduction system on a moving member must be established q=y. Where the reduced materiality can be determined from the conditions ^{[6]}

(1) |

where is:

*m**(*q*): generalized materiality of system,

*m*_{i}: the materiality of the member *i* of executing displacement motion system,

*v*_{i}: his velocity,

*I*_{j}: the moment of inertia of the member *j* of the system executing rotational movement to the axis of rotation,

*ω*_{j}: the size of angular velocity of the member *j*,

*m*_{k}: the weight of the member *k* of the system executing the general plane motion,

*v*_{Tk}: the size of the velocity of gravity of the member *k*,

*I*_{Tk}: the moment of inertia of the member *k* of the axis of rotation passing through the center of gravity,

*ω*_{k}: the angular velocity of the member *k*.

**Fig**

**ure**

**1.**The cam mechanism

For a system with a constant ratio is *m**=konst. and the motion equation is simplified to the form:

(2) |

The reduced materiality can be determined from the conditions in our case:

(3) |

After the correct adjustments it can get:

(4) |

(5) |

(6) |

where is after the adjustments for reduced materiality and force considering the relationship between the geometric and kinematical variables as:

(7) |

(8) |

(9) |

(10) |

(11) |

Reduced power we can determine from the equality of virtual powers:

(12) |

After substituting the relations between geometric and kinematical variables and then after the correct modification it gets:

(13) |

(14) |

Because of it is a mechanism of variable ratio - and the motion equation has the form:

(15) |

Where is:

(16) |

(17) |

Considering a is the resulting equation of third member following:

(18) |

That final equation of motion can be processed by using a mathematical program Matlab and Simulink.

### 3. Analyses Using MSC Adams Program

**Figure**

**2.**The cam mechanism model in MSC Adams/View

**Figure**

**3**

**.**The cam mechanism – spatial view

With MSC Adams software users can produce virtual prototypes to simulate complex mechanical systems and quickly analyze multiple design variations until an optimal design is achieved. MSC Adams is one of many computer programs for modeling and simulating multi body systems. In programs a virtual prototype of a mechanism show in Figure 2 and Figure 3 can be built and then simulated.

If the results, a certain movement or load transmission are not satisfy, the prototype can easily be modified and then simulated again.

Adams is the world’s most widely used multi-body dynamics simulation software. It lets you build and test virtual prototypes, realistically simulating on your computer, both visually and mathematically, the full–motion behavior of your complex mechanical system designs as shown in the Figure 4.

**Figure**

**4**

**.**The joints of the cam mechanism

The software checks your model and automatically formulates and solves the equations of motion for kinematical, static, quasi-static, or dynamic simulations ^{[4]}. It is also an appropriate tool for the development of miniature mechatronic elements as well as the examination of complex systems.

**Figure**

**5**

**.**The translational displacement of the follower

**Figure**

**6**

**.**The translational velocity of the follower

**Figure**

**7**

**.**The translational acceleration of the follower

After fabrication model in MSC Adams/View shown in Figure 2 we could try to simulate the movement of the cam mechanism and to determine the physical properties of our selected third member, lifter in our case. The Post Processor processes the results of the solution. We have chosen necessary interested variables such as path, velocity and acceleration. The next step was to choose the correct folder where variables are investigated. Graphs of the path, velocity and acceleration using the MSC Adams program are shown on Figure 5, Figure 6 and Figure 7 ^{[5, 6]}.

The Postprocessor provides complete value at certain time intervals and of course the specific waveforms from which can be read values. We have chosen the TIME and y-DATA of required physical variables in Database window-Navigator (Figure 9) ^{[3]}.

The last step of dynamic analysis of cam mechanism was to find out some forces which operate in spring and also in pin labeled as a point A when is the cam mechanisms in motion. The size and the course of force of spring and also the course of force of pin are shown in Figure 10 and Figure 11 ^{[4]}.

**Figure**

**8**

**.**The postprocesor window with the animation model in certain position

**Figure**

**9**

**.**Database Navigator

**Figure**

**10**

**.**The result parameters of the force spring in cam mechanism with dependence of the time

**Figure**

**11**

**.**The result parameters of the spring deformation in cam mechanism with dependence of the time

**Figure**

**12**

**.**The result parameters of the translational displacement of the member No.3 cam mechanism with dependence of the time

**Figure**

**13**

**.**The result parameters of the translational velocity of the member No.3 cam mechanism with dependence of the time

### 4. Conclusion

The evaluation of the results, especially the specific values of the displacement, velocity and acceleration the lifter is so difficult without additional equipment, which together with the cam mechanism consists of a functional unit complex. It's caused because the value of the displacement, velocity and acceleration are known at each time of the lifter, but we don't know if these values are satisfactory. If is the size of lift created by this mechanism is sufficient to ensure the proper function of the made whole, for instance. The designed cam mechanism could be used in practice, for example in agricultural machineries or everywhere where is needed to change move while the output parameters of the cam mechanisms are simultaneously suitable. The graphical course of displacement, velocity and acceleration is suggested to show us the correct function of cam mechanism. One of the advantages of the cam mechanism is his simplicity against that complex shaped cam mechanism in which the production is considerably difficult.

### Acknowledgement

This work was supported by the Ministry of Education of the Slovakia Foundation under Grant VEGA No. 1/0289/11, VEGA No. 1/1205/12 and VEGA No. 1/0937/12 and APVV-0091-11.

### References

[1] | Frankovský, Peter; Delyová, Ingrid; Hroncová, Darina; “Kinematic analysis of movement of a point of a simple mechanism” 4^{th} International Conference Modelling of mechanical and mechatronics systems, KAMaM, Technical university Košice, Herľany, 2011, Slovakia, s.53-58. | ||

In article | |||

[2] | Frankovský, Peter; Delyová, Ingrid; Hroncová, Darina;. “Dynamická analýza modelu mechanického systému v simulačnom prostredí MATLABSimMechanics”. In: ATP Journal plus. Č. 1, 2012, s. 6-9. | ||

In article | |||

[3] | Hroncová, Darina; Binda, Michal; Šarga, Patrik; Kičák, František; “Kinematical Analysis of Crank Slider Mechanism Using MSC AdamsView”, In: Procedia Engineering : MMaMS 2012: Modelling of Mechanical and Mechatronics Systems 2012: November 6th-8th 2012, Zemplínska Šírava, Slovakia. - Košice : TU, 2012 Vol. 48, p. 213-222. | ||

In article | |||

[4] | https://www.mscsoftware.com/product/adams | ||

In article | |||

[5] | Bocko, Jozef; Frankovský, Peter; Delyová, Ingrid; PÁSTOR, Miroslav; Kinematika v príkladoch, SjF TU v Košiciach, 2011. | ||

In article | |||

[6] | Záhorec, Ondrej, Caban, Slavomír: Aplikovaná mechanika. Košice: TUKE, 1992. 456 s. | ||

In article | |||