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Finite element modeling of a polyarticulated robotic system.


The robotic system is composed from two units, one with a flexible structure with kinematic possibilities similar with the snake's locomotion and another one for driving.

The flexible unit is composed from three modules with independent driving, that confers a complex 3D configuration, with multiple kinematic possibilities for the working space.

The flexible structure is conceived in modular systems with decoupling possibilities for a controlled optimization of the working space.

The flexible structure as an integrate system, or as independent modules, is conceived to allow driving in two modes, respectively:

--one with wires and a flexible central column;

--one with flexible vertebrates and a flexible central column;

For the case in which the driving is made by wires, a module has two degrees of freedom and in the case of driving with flexible columns each module has three degrees of freedom.

The driving unit is obvious structured in three modules for controlling a complex workspace, with multiple kinematic possibilities.

The mechanical structure for each module is based upon thread transmissions with self decelerations possibilities and adjust of the axial-radial clearances.

The flexible unit with the snake-like design is composed from a base flange, some intermediary flanges, and four flexible shafts, with high elasticity which will be called vertebral spines. The central shaft is mounted rigidly to all the intermediary flanges, fig. 1.

The three super elastic spines are mounted equidistantly upon the central spine.

The entire vertebrates are connected only to the end flange. The intermediary flanges maintain constant the radial distance between the secondary tubes and the central vertebrate.

Changing in an active way the length of two of the vertebrate spines, the final flange can be manipulated with two degrees of freedom in any direction.

The three actuating spines are rigidly joined only to the end flange; the joint between them and the intermediary flanges is like one translational joint.




As it was presented above, the robot is designed in a modular structure, with three modules, independently actuated through thread transmissions with possibility to adjust the radial and axial clearances, with the aim to assure the imposed kinematics precision.

The vertebrate unit is designed to work in two ways, respectively with two or three degrees of freedom on each module.

The flexible unit has a cylindrical form, composed from three modules in order to assure a complex workspace.



The assembled experimental model:



To demonstrate the viability of mechanical system it is proposed the functionality of the modeling and simulation with finite element method.

Faithfully are respected the shape conditions and loadings, so that through a Virtual Prototyping a parameterized virtual system is obtained, which can be loaded in order to get various types of deformed shapes, obviously controlled for the analyzed mechanical system.

Parameterized modeling of the flexible system allows 3D simulation for different variants with one, two or three modules, with different size dimensions and types of materials with circular vertebras full or tubular, in this way assuring a wider area of skills for the proposed and analyzed system.



1. The three modules that define the robotic system provide more freedom degrees and therefore a complex spatial configuration of working space.

2. Experimental model has showed that the command and control of the flexible system are optimal when the flexible vertebras are operated by pulling and pushing.

3. Parameterized modeling and finite element analysis allow total control of flexible unit behavior in the dynamic regime from the point of view of the trips, stress and strains.

4. Presented robotic system can be adapted for multiple applications in industries or on small scale in minimal invasive surgery.

5. In the near future we will built, using almost the same principle, a tronconic form of our robot that will be actuated in real-time in 3-D space.


Hirose, S. (1993). Biologically Inspired Robots, Snake-Like Locomotors and Manipulators, Oxford University Press.

Li, C. & Rhan, C. (2002). Design of Continuous Backbone, Cable-Driven Robots, ASME Journal of Mechanical Design, vol. 124, pp 265-271

Simaan, N.; Taylor, R. & Flint, P. (2004). A Dexterous System for Laryngeal Surgery--Multi-Backbone Bending Snakelike Slaves for Teleoperated Dexterous Surgical Tool Manipulation, IEEE International Conference on Robotics and Automation, New Orleans, pp 351-357

Zanganeh, K. & Angeles, J. (1995). The Inverse Kinematics of Hyper-Redundant Manipulators Using Splines, IEEE International Conference on Robotics and Automation, pp. 2797-2802.

Yoshikawa, T. (1990). Foundations of Robotics Analysis and Control, MIT Press

*** IDEI, Driving of Tentacular Robots Based on Artificial Vision, Contract n. 102/01.10.2007
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Author:Dumitru, Sorin; Cojocaru, Dorian; Dumitru, Nicolae; Ciupitu, Ion; Geonea, Ionut; Dumitru, Violeta
Publication:Annals of DAAAM & Proceedings
Article Type:Report
Geographic Code:4EUAU
Date:Jan 1, 2009
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