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Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 111
Author(s):  
You Li ◽  
Haizhao Liang

Robust finite-time control algorithms for satellite attitude maneuvers are proposed in this paper. The standard sliding mode is modified, hence the inherent robustness could be maintained, and this fixed sliding mode is modified to dynamic, therefore the finite-time stability could be achieved. First, the finite -time sliding mode based on attitude quaternion is proposed and the loose finite-time stability is achieved by enlarging the sliding mode parameter. In order to get the strict finite-time stability, a sliding mode based on the Euler axis is then given. The fixed norm property of the Euler axis is used, and a sliding mode parameter without singularity issue is achieved. System performance near the equilibrium point is largely improved by the proposed sliding modes. The singularity issue of finite-time control is solved by the property of rotation around a fixed axis. System finite-time stability and robustness are analyzed by the Lyapunov method. The superiority of proposed controllers and system robustness to some typical perturbations such as disturbance torque, model uncertainty and actuator error are demonstrated by simulation results.


2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Nguyen Van Dang

The static bending analysis of the FG porous beam resting on the two-parameter elastic foundation is initially carried out using a combination of Reddy’s high-order shear deformation theory and the finite element technique, where the initial geometrical imperfection and rotation movement in one fixed axis are calculated. Through the power-law distribution function with porosities, material characteristics vary constantly from one surface to the next in the direction of thickness, and the beam is concurrently impacted by an acting force perpendicular to the beam axis and an axial compressive force. The stiffness matrix of the beam element changes as a result, and the static bending response of this beam is significantly different from that of ordinary beams. Comparison cases with published findings are used to verify the computational theory. The calculations clearly reveal many innovations for rotating beams that are influenced by many different kinds of loads, which may be used to the designing, manufacturing, and usage of these structures in reality.


2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Pete Hwang ◽  
Danilo JR Tadeo

Tangential velocity is a concept that is often taught as a part of rotation, and is the linear velocity an object has as it turns about a fixed axis. The main goal of this research project was to examine this concept and demonstrate it on a self-coded robot. The robot was designed with two rotating motors with two wings of different lengths to be attached on top, and the motors were connected to a circuit board and coded using the programming language C to rotate with equal and constant angular velocities upon initiation. The main hypothesis is that the length of rotating wings is directly proportional to the tangential velocity of the wings. The project provides a new way of demonstrating tangential velocity in a high school physics class.


2021 ◽  
Author(s):  
Patrick Fluckiger ◽  
Simon Henein ◽  
Ilan Vardi ◽  
Hubert Schneegans ◽  
Loïc Tissot-Daguette

This paper presents innovative mechanisms capable of advantageously providing attitude control for spacecrafts. These new mechanisms, which we have named flexure wheels, are the dynamic equivalent of a rotating wheel and can be entirely implemented with flexures.A reaction wheel is a well known device for controlling the orientation of spacecrafts. It consists in a motorised fly-wheel which is placed within the spacecraft. To set the wheel into angular rotation, a torque is applied to the wheel which in response applies the opposite torque back to the spacecraft, according to Newton's third law. This reaction torque is how the spacecraft rotates in order to control its orientation. In order to enable this wheel to rotate around a fixed axis, several methods have been implemented such as ball bearings, which suffer from frictional losses and imperfections which lead to vibrations and failure, as well as magnetic bearings which do not suffer from these issues but have an increased power consumption and complexity.The subject of this paper is to introduce alternative mechanisms that are able to produce the same constant angular momentum as a rotating wheel, but which do not suffer from the above defects.In order to reach this goal, our inventions use flexure mechanisms to produce the required constant angular momentum. Note that the term flexure mechanism is exactly equivalent to compliant mechanism. The difficulty in this task is that flexures only have a limited stroke making it virtually impossible for a flexure bearing wheel to rotate around a fixed axis with constant angular momentum. We therefore found alternate methods for generating angular momentum by using flexure mechanisms.Two methods are presented in this paper. The first consists of a rigid body whose centre of mass has a circular trajectory around a fixed point, but the body does not rotate around its centre of mass. The body moves in translation and acts dynamically as a point mass, and thereby generates angular momentum in a constant direction. The second consists of two bodies rotating around their centres of mass, but whose total angular momentum lies in a fixed direction. The first method was successfully exploited in the IsoSpring project whose goal was to introduce new two degree of freedom oscillators in mechanical clocks and watches, in order to remove their traditional escapement mechanism. The second mechanism is also inspired from the IsoSpring project where a sphere oscillating around its centre of mass provided a two degree of freedom oscillator less sensitive to the direction of gravity.The paper presents flexure wheel designs along with their implementations. Moreover, methods to control the uniform circular motion are presented, among which a novel flexure bearing which restricts the motion of a body to translation on a circular orbit. Two prototypes were successfully built and tested. Finally, qualitative results from this proof of concept are presented.


2021 ◽  
Author(s):  
Mahesh Chavan ◽  
Dnyaneshwar Kapase ◽  
Manish Parachande ◽  
Shambhu Hingmire ◽  
Mahesh Gund ◽  
...  

The stirrer of conventional machine rotates in one direction only which creates a specific flow pattern within the fluids hence the particles tend to stay to the walls of container owing to the force instead of mixing thoroughly in mixture of paint, ultimately results into poor quality mixture of paints there by poor quality output of paint . In order to possess a through mixing of metal oxide powder it might be appropriate to possess a stirrer that rotates such rotates about own axis also revolves about another fixed axis which helps it reach all parts of the container. This ensures that turbulence required for thorough mixing is provided all over the container. It would be advantageous to vary pattern of flow, which avoids vortex formation, i.e. motion of particles in a spiral path. Also if a wiper is added that brings the particles adhering to walls of container back to main flow or mixing area, good quality mixture are going to be ensured. The planetary mixer with strainer may be a perfect solution that has all the above mentioned features. This machine involves a rotating stirrer that revolves about the fixed container axis also as incorporates an strainer that changes the flow pattern and also acts as a wiper. Machine has variable mixing speed feature at an equivalent time delivers heavy torque to the stirrer for proper mixing.


2020 ◽  
Vol 75 (5) ◽  
pp. 447-450
Author(s):  
A. Aknouch ◽  
Y. Elouardi ◽  
M. Mouhib ◽  
R. Sebihi ◽  
A. Didi ◽  
...  

2020 ◽  
Vol 12 (2) ◽  
pp. 151-161
Author(s):  
M. RAJA ◽  
Ugur GUVEN ◽  
Kartikay SINGH

Navigation and guidance systems for most automobile as well as aerospace applications require a coupled chip setup known as Inertial Measurement Units (IMU) which, depending on the degree of freedoms, contains a Gyroscope (for maintaining orientation and angular velocity), Accelerometers (to determine acceleration in the respective direction) and a Magnetometer (to determine the respective magnetic fields). In the three-dimensional space, any required rotation analysis is limited to the coordinate systems and all subtended angles in either direction must be defined by a fixed axis to effectively estimate the stability and to define all the attitude estimates needed to compile different rotations and orientations. The Quaternions are mathematical notations used for defining rotations and orientation in three-dimensional space. The simplest terms Quaternions are impossible to visualize in a three-dimensional space; the first three terms will be identical to the coordinate system, but through Quaternions another vector quantity is added into the equations, which may in fact underline how we can account for all rotational quantities. The fundamental analysis of these components different applications for various fields is proposed.


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