Prof. Nir Schwalb and Dr. Oded Medina showed that not only the number of links and axes determines the movement in a mechanism, but also their geometric arrangement in space, and also discovered "hypo-paradoxical" mechanisms that lock even though, according to the classical formula, they were supposed to move.
Since it was first presented in 1904 by engineer George Bennett, the Bennett Mechanism has been considered a paradox: a structure that is supposed to be rigid and completely static according to all accepted calculation formulas, but in reality exhibits smooth and continuous motion. Now, new research by Prof. Nir Schwalb and Dr. Oded Medina from the Faculty of Engineering at Ariel University offers for the first time a comprehensive theoretical framework that explains the phenomenon and reveals a new world of "impossible" mechanisms.
The Roots of the Mystery: When the Mobility Formula Fails
To understand the magnitude of the achievement, one must go back to the basics of mechanical theory. In 1883, the "mobility formula" (known as the Chebyshev-Grubler-Kutzbach formula) was formulated, which allows engineers to predict how many degrees of freedom a given mechanism will have based on the number of links and axes. Bennett's mechanism consists of four rigid links connected by four non-parallel and non-intersecting axes of rotation.
According to dry calculations, such a structure is an "overconstrained system," meaning it should be impossible to move. In fact, mathematics predicts that even assembling the mechanism would be impossible without bending or applying force to the material. In reality, however, when certain geometric relationships between the lengths of the links and the angles of the axes are maintained, the mechanism moves with complete freedom. Over the past 120 years, many researchers have tried to explain why the mechanism "violates" the laws, which has earned it the nickname "paradoxical mechanism."
The research breakthrough
In their study, published in the prestigious journal Mechanism and Machine Theory, Prof. Nir Schwalb and Dr. Oded Medina decided to abandon the specific approach to the Bennett mechanism and examine a much broader family of closed spatial mechanisms. To do this, they used Screw Theory, a mathematical field that describes spatial motion through a unified representation of rotation and displacement.
The researchers examined a broad family of closed spatial mechanisms and examined when the calculated number of degrees of freedom agrees with the actual movement, and when it does not, alongside a geometric analysis of the arrangement of the axes in space.
"The classical formula examines the quantity, how many connections and how many links there are in the system," explains Prof. Shvelev, head of the Department of Industrial Engineering and Management at Ariel University. "It doesn't really see the spatial shape that is created between them. Our research has shown that the geometric arrangement of the axes is the decisive factor. Sometimes the geometry creates internal dependencies between the constraints, so that they cancel each other out and allow the system to move despite the excess connections."
The most surprising discovery in the study was the existence of an opposite phenomenon: mechanisms that, according to the formula, were supposed to move freely, but due to a certain geometric arrangement remained completely locked. For them, the researchers coined the term "hypoparadoxical mechanisms," thereby proving that the "Bennett paradox" is not an isolated case, but part of a broad and unknown system of kinematic laws.
From Theory to Reality: Research Driving Industrial Innovation
For the scientific community, the ripples of this research have great practical significance. A precise understanding of the relationship between geometry and motion is essential for developing the next generation of:
- Medical robotics – creating tiny, precise joints for minimally invasive surgeries.
- Aerospace – Designing antennas and foldable structures for satellites, which must operate with maximum reliability with a minimum of engines.
- Industrial production – designing mechanisms with fewer moving components, which reduces wear and tear and production costs.
In an era where technological innovation is reshaping society, fundamental engineering research plays a crucial role in creating advanced solutions that impact many areas of life. The research is not just a solution to a historical puzzle, but also laying a new foundation for modern mechanical design.
The university, which operates advanced laboratories in the fields of robotics, control, and kinematics, encourages an interdisciplinary approach that allows researchers to tackle fundamental questions that remain unanswered in the global academic world.
The Faculty of Engineering at Ariel University emphasizes the combination of in-depth theory and field applications, with the work of the research teams permeating the world of industry, medicine, and technology, and driving processes of development, optimization, and improvement of complex systems in Israel and around the world.
2 תגובות
Well done to the researchers.
Respect for the university.
Give a drawing, a painting, a picture, to demonstrate what it is. Right now the article is closed to me.