Reconfigurable/Foldable Overconstrained Mechanism and Its Application

The paper presents some possible applications started from a six revolute joints (6R) overconstrained mechanism. The spatial devices obtained are based on the 6R Wohlhart symmetric mechanism in a special spatial position, with three non-adjacent joints constrained to remain in a fixed plane. This special spatial disposition allows us to obtain some reconfigurable/foldable devices, with an estimated application in the automotive industry field.

Research of Near-Wellbore Fracture Morphology, Formation Mechanism, and Propagation Law for Different Perforation Modes During the Perforation Process

Perforation plays an important role in the fracture morphology near the wellbore and the propagation of hydraulic fracturing fractures. Therefore, it is of great significance to find out the fracture morphology and propagation law during perforation for optimizing perforation technology, enhancing fracture control, and realizing complementary advantages of different perforation schemes. Based on analyzing the characteristics of perforation fracturing at each stage and existing perforation technology, two types of deep-penetrating perforating bullets were used to carry out large-scale perforation shooting experiments. The real processes of spiral perforation, directional perforation, conventional fixed-plane perforation, and interlaced fixed-plane perforation were simulated, respectively. The near-wellbore fracture morphology, formation mechanism, and propagation rule during perforation with different perforation modes were analyzed. The results show that (1) perforation is accompanied by the formation of tunnels, and there are three kinds of source microfractures developed around the tunnels, namely Type I radial microfractures, Type II oblique microfractures, and Type III perforation tip divergent microfractures. The three microfractures are interconnected to form more complex near-wellbore fractures. (2) Under different perforation modes and parameters, the near-wellbore fracture morphology and propagation law formed by microfractures around tunnels are also different. (3) The existence and expansion of near-wellbore fractures validate Chen et al.’s (2005) conjecture that there are “pre-existing fractures” in perforation and negate the assumption that the perforation tunnels are complete. There are no near-wellbore fractures when the perforation method is optimized. The research results in this paper can provide guidance and reference for improving the perforation fracturing effect in oil and gas reservoirs.

Qualitative Analysis of Some Libration Points in the Restricted Four-body Problem

We consider the situation where three heavy gravitational bodies form the Lagrange configuration rotating in a fixed plane and the fourth body of negligible mass moves in this plane. We present three cases of so-called libration points and we study their stability using linear approximation and KAM theory. In some situations we prove the Lyapunov stability for generic values of some parameter of the problem.

About Symmetry in Partially Hinged Composite Plates

We consider a partially hinged composite plate problem and we investigate qualitative properties, e.g. symmetry and monotonicity, of the eigenfunction corresponding to the density minimizing the first eigenvalue. The analysis is performed by showing related properties of the Green function of the operator and by applying polarization with respect to a fixed plane. As a by-product of the study, we obtain a Hopf type boundary lemma for the operator having its own theoretical interest. The statements are complemented by numerical results.

MATHEMATICAL MODEL OF THE ESTIMATION OF THE EFFICIENCY OF THE CONTROL OF RADIO ELECTRONIC COUNTERACTION OF THE AIRPORT STATION OF ACTIVE CONTEMPORARY INTERFERENCES IN THE CONDITIONS OF CREATING A POLARIZATION INTERFACE ON A FIXED PLANE OF IT

In the article, based on the analysis of the use of modern individual on-board electronics and electronic search and guidance systems, it is concluded that one of the promising directions for their further development is the search for methods of not only protection from the means of radio-electronic suppression, but also an active counteraction to these means, the so-called counter-radio electronic counteraction One of the most effective obstacles that can be created by radar detection systems by stations is the active barrier of individual enemy protection - this is a polarizing obstacle, so the issue of reducing the effectiveness of the polarizing effect on the system of automatic support for the direction of the on-board radar weapon control system is quite relevant today. In order to counteract the station's active interference in the conditions of its creation of a polarization obstacle, it is proposed to change the plane of polarization on the receiving side. As a result, a useful signal will be taken in polarization, which does not coincide with the polarization plane of the radiation signal. Failure to match polarization when receiving a reflected signal will not significantly affect the power of a useful signal. In order to implement the proposed method in the article, a mathematical model for evaluating the effectiveness of the counter-radio-electronic counteraction of the on-board station was proposed to obstruct the enemy's individual protection in the conditions of its creation of a polarization obstacle on a fixed plane of polarization, as well as features of the practical realization of such counteraction during air combat and restrictions on its creation. The mathematical model of the evaluation of the effectiveness of the counter-electronic counteraction to the aircraft station's active barriers in the conditions of its creation of a polarization obstacle on a fixed plane of polarization is developed, it will allow to formulate practical recommendations regarding the application of the developed method at different stages of air combat. KELP management in different ways, on the one hand, slightly reduces the effectiveness of the on-board management of weapons at different stages of flight, but on the other hand, the effectiveness of the airborne equipment of the airborne ejection of the enemy significantly decreases, which will increase the effectiveness of the use of weapons and the likelihood of damage to the enemy aircraft using the means of destruction, which today have a significant cost.

Mechanical model of muscle contraction 2. Kinematic and dynamic aspects of a myosin II head during the working stroke

The condition of a myosin II head during which force and movement are generated is commonly referred to as Working Stroke (WS). During the WS, the myosin head is mechanically modelled by 3 two by two articulated segments, the motor domain (S1a) strongly fixed to an actin molecule, the lever (S1b) on which a motor moment is exerted, and the rod (S2) pulling the myosin filament (Mfil). When the half-sarcomere (hs) is shortened or lengthened by a few nanometers, it is assumed that the lever of a myosin head in WS state moves in a fixed plane including the longitudinal axis of the actin filament (Afil). As a result, the 5 rigid segments, i.e. Afil, S1a, S1b, S2 and Mfil, follow deterministic and configurable trajectories. The orientation of S1b in the fixed plane is characterized by the angle θ. After deriving the geometric equations singularizing the WS state, we obtain an analytical relationship between the hs shortening velocity (u) and the angular velocity of the lever . The principles of classical mechanics applied to the 3 solids, S1a, S1b and S2, lead to a relationship between the motor moment exerted on the lever (MB) and the tangential force dragging the actin filament (TA). We distinguish θup and θdown, the two boundaries framing the angle θ during the WS, relating to up and down conformations. With the usual data assigned to the cross-bridge elements, a linearization procedure of the relationships between u and , on the one hand, and between MB and TA, on the other hand, is performed. This algorithmic optimization leads to theoretical values of θup and θdown equal to +28° (−28°) and −42° (+42°) respectively with a variability of ±5° in a hs on the right (left), data in accordance with the commonly accepted experimental values for vertebrate muscle fibers.

Car Jack Based on 6R Overconstrained Mechanism

The paper presents a possible practical application based on two 6R overconstrained mechanism, more precisely 6R Wohlhart overconstrained mechanism. Two of these mechanisms are put in a mirror position, in order to obtain a car jack. The mechanisms are disposed in other position than the original one, three non-adjacent joints being constrained to remain in a fixed plane.

The Use of Projective Geometry on the Mechanism System Motion and Stability of the Special Problems in Judgement

In a principle of kinematics, when a rigid body is motion in a plane, and the fixed plane only the presence of a speed zero point -- the instantaneous center of velocity. In the mechanism of two rigid bodies be connected by two parallel connection links, why can the continuous relative translation? Where is the instantaneous center of velocity? ... ... The traditional Euclidean geometry theory can’t explain these phenomenon, must use projective geometry theory to solve. The actual motion of the mechanism is disproof in Euclidean geometry principle limitation. This paper introduces the required in projective geometry basic proof of principle, and applied to a specific problem.