MATHEMATICAL MODEL OF TWO-DOF FIVE LINKS CLOSED-CHAIN MECHANISM (PANTOGRAPH)

Document Type : Original Article

Authors

1 Mechatronics Engineering Department, Faculty of Engineering, MTI University, Cairo, Egypt

2 Mechanical Engineering, Faculty of Engineering, Future University in Egypt

3 Mechatronics Engineering Department, Faculty of Engineering, Egyptian-Chinese University (on leave from Helwan University).

4 Higher Engineering Institute, Thebes Academy, Cairo, Egypt, (on leave from Helwan University)

Abstract

Parallel manipulators have been developed largely for applications that need high accuracy and speed, which make them useful in important fields. This paper presents a detailed mathematical model for a closed chain pantograph mechanism. This task was done by defining its differential equation of motion and implements it using the Matlab Simulink. The mathematical model describes the forward and inverse kinematics, in addition, the dynamic behavior. The mathematical model advantage is studying the parameters variation using different advanced control techniques. This model can be implemented using the Simscape model, which considers a black-box model. To validate the proposed mathematical model for the pantograph, the corresponding model mechanism using the Simscape had been implemented. A comparative study was executed between the mathematical model and the outputs of the Simscape. The results indicated a perfect match for output extracted from Simscape and Simulink. This is evidence for the validity of the inferred equations and Simulink model.

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