Mathematical Model of a Ring-Involute-Teeth Spherical Gear with a Double Degree of Freedom

2002 ◽  
Vol 20 (12) ◽  
pp. 865-870 ◽  
Author(s):  
S.-C. Yang
Keyword(s):  
Mathematical Model ◽  
Degree Of Freedom ◽  
Double Degree ◽  
Spherical Gear

Using a planar rack cutter with variable modulus to generate a spherical gear pair

2020 ◽  
Vol 44 (1) ◽  
pp. 108-120
Author(s):  
Hsueh-Cheng Yang ◽  
Chih-Yao Sun
Keyword(s):  
Mathematical Model ◽  
Degree Of Freedom ◽  
Gear Pair ◽  
Tooth Contact Analysis ◽  
The Family ◽  
Variable Modulus ◽  
Double Degree ◽  
Relationship Of ◽  
The Mathematical Model ◽  
Spherical Gear

In this study, an imaginary planar rack cutter with variable modulus and discrete conical teeth was used to generate a spherical gear pair with double degree of freedom. First, a geometric method was used to design the mathematical model of the imaginary planar rack cutter with variable modulus and discrete conical teeth. Next, the relationship of coordinate systems between the generating and generated surfaces was established. Then, the family of the imaginary planar rack cutter surfaces was obtained by homogeneous coordinate transformation matrix. Further, two equations of meshing between the generating and generated surfaces were determined by the two-parameter envelope theory. The mathematical model of spherical gear pair with variable modulus and discrete ring-involute teeth can be created by using the two equations of meshing and the family of the imaginary planar rack cutter surfaces. The mathematical models of the spherical gear pair with double degree of freedom and tooth contact analysis method were used to investigate the assembly errors of the gear pair in four cases.

A geometric model of a spherical gear with a double degree of freedom

2002 ◽  
Vol 123 (2) ◽  
pp. 219-224 ◽  
Author(s):  
Shyue-Cheng Yang ◽  
Chaò-Kuang Chen ◽  
Ke-Yang Li
Keyword(s):  
Geometric Model ◽  
Degree Of Freedom ◽  
Double Degree ◽  
Spherical Gear

Compact 2DOF liner based on a long elastic open-neck acoustic resonator for low frequency absorption

2021 ◽  
Vol 69 (1) ◽  
pp. 1-17
Author(s):  
Frank Simon ◽  
Delphine Sebbane ◽  
surname given-names
Keyword(s):  
Low Frequency ◽  
Acoustic Resonator ◽  
Degree Of Freedom ◽  
Tube Length ◽  
Remarkable Feature ◽  
Absorption Frequency ◽  
Acoustic Liners ◽  
Quarter Wavelength ◽  
Resonance Frequencies ◽  
Double Degree

Passive acoustic liners, used in aeronautic engine nacelles to reduce radiated fan noise, have a quarter-wavelength behavior. The simplest systems are SDOF-type (single degree of freedom), consisting of a perforated sheet backed with a honeycomb, whose absorption ability is limited to frequencies near the Helmholtz frequency. Thus, to widen the absorption frequency range, manufacturers use a 2DOF (double degree of freedom) system, with an internal layer over another honeycomb (stack of two resonators). However, one constraint is the limited thickness of the overall system, which reduces the space allotted to each honeycomb. A possible approach, based on a previous concept called LEONAR (long elastic open-neck acoustic resonator), could be to link each perforated layer to hollow tubes inserted in each honeycomb layer, in order to shift resonance frequencies to lower frequencies by extending the air column lengths. The presence of an empty chamber on both sides of the internal perforated layer also allows the tube length to be increased through tubes crossing both cavities, preserving the liner thickness. The main aim of this article is to mathematically describe the principle of a 2DOF LEONAR and to show the relevance of the mathematical model through FEM simulations and experiments performed in an impedance tube. Moreover, its behavior is analyzed through a parametric study, in order to explore its potential for an aeronautic application. A remarkable feature of 2DOF LEONAR-type materials with insertion of bottom tubes in the higher cavity is the possibility of maintaining the low frequency band provided by the original LEONAR concept, while adding a second absorption peak at a higher frequency, by the second layer and the accompanying tubes. There is a fundamental difference from classical SDOF/2DOF resonators, for which the thicknesses are obviously different.

Relationship between the Steady-Handling Characteristics of Automobiles and Their Stability

1973 ◽  
Vol 15 (5) ◽  
pp. 326-328 ◽  
Author(s):  
R. S. Sharp
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Degree Of Freedom ◽  
Nonlinear Region ◽  
Handling Characteristics ◽  
Yield Information ◽  
Turning Motion ◽  
The Stability ◽  
Three Degree Of Freedom

Analyses of the steady-state handling behaviour of an automobile and the stability of its steady-turning motion, based on a three degree of freedom mathematical model, are used to show that the steady behaviour and the stability are related similarly in the nonlinear region as in the well documented linear one. It is concluded that analysis and measurement of the steady behaviour will yield information on the stability of automobiles.

Optimal Design of a Six-Bar Linkage for an Anthropomorphic Three-Jointed Finger Mechanism

1992 ◽  
Author(s):  
Jichuan Zhang ◽  
Gongliang Guo ◽  
William A. Gruver
Keyword(s):  
Mathematical Model ◽  
Nonlinear Programming ◽  
Optimal Design ◽  
Transmission Efficiency ◽  
Degree Of Freedom ◽  
Optimal Parameters ◽  
Joint Friction ◽  
Robotic Devices ◽  
End Effectors ◽  
Human Finger

Abstract We treat the design of a three-jointed, anthropomorphic, finger mechanism for prostheses and robotic end-effectors. Based on the study of configurations for the human finger, we propose a six-bar linkage with one degree of freedom for the finger mechanism. A model of the fingertip displacement of the mechanism is derived by a vector analysis approach. We study the effects of joint friction on the transmission efficiency. By measuring the joint positions of a human finger, we develop a mathematical model of the pinching and holding configurations for the human finger. Optimal parameters for the finger mechanism are obtained by nonlinear programming based on motion posture, locus, transmission efficiency, and weight subject to geometric and bionic constraints. Simulations indicate that the mechanism is useful in a variety of prosthetic and robotic devices.

The Effect of Gravity and Rotor Configuration on Dry Friction Whip and Safe Rotor/Stator Clearance

2019 ◽  
Author(s):  
Rajiv Kumar Vashisht
Keyword(s):  
Mathematical Model ◽  
Fault Diagnosis ◽  
Dry Friction ◽  
Rotating Machinery ◽  
Degree Of Freedom ◽  
System Response ◽  
Rich Variety ◽  
Wide Range ◽  
Clearance Level ◽  
High Degree

Abstract A mathematical model is developed for a real rotor/stator system with high degrees-of-freedoms, multiple disks, flexible bearing supports and couplings. The safe clearance level for coasting up of the rotor is calculated for a general high degree-of-freedom rotor/stator system. The harmful phenomena of dry friction whip, which is generally observable for simple 2 degree-of-freedom Jeffcott rotors in the absence of gravity only, can be proved to exist (in real rotor/stator systems) even in the presence of gravity for a wide range of clearance levels. In case of Jeffcott rotors, by fixing the clearance and increasing the rotor spin frequency, the response of the system follows the pattern: No rub - Forward Annular Rub (FAR) - Partial Forward Whirl (PFW) - Partial Backward Whirl (PBW) - dry whip (WHIP). In case of a real rotor/stator system, at certain frequencies, the system directly jumps to dry whip. The simulated results show a rich variety of system dynamics including FAR, PFW and WHIP in case of vertical rotors where the effect of gravity is neglected. For horizontal rotors, under the effect of gravity, the system response contains multi-harmonics, chaotic responses and multi-period vibrations. Based on these responses, a robust fault diagnosis strategy can be designed to identify the rubbing action in rotating machinery.

Research on Position Keeping and Path Following Strategy for the Under-Actuated Waved Glider

2020 ◽  
Author(s):  
Peng Wang ◽  
Xinliang Tian ◽  
Xiantao Zhang ◽  
Daoyong Wang ◽  
Xiaoxian Guo
Keyword(s):  
Mathematical Model ◽  
Surface Waves ◽  
Path Following ◽  
Degree Of Freedom ◽  
Environmental Disturbances ◽  
Autonomous Surface Vehicle ◽  
Wave Glider

Abstract Wave glider is a novel autonomous surface vehicle that uses energy from surface waves for propulsion. However, because it is inherently under-actuated, multi-variable and strong coupled, it is challenging to control the wave glider accurately under the environmental disturbances. In this study, a novel robust position keeping guidance strategy and an advanced path following approach for the under-actuated wave glider based on restricted circle are firstly developed. Furthermore, an 8-DOFs (Degree-of-Freedom) mathematical model for the under-actuated wave glider is adopted, and the position keeping and path following tasks of the wave glider are conducted in simulation. The results demonstrate that the under-actuated wave glider is able to accomplish the position keeping and path following tasks with the proposed strategies.

Mathematical Model of Worm-like Motion Systems with Finite and Infinite Degree of Freedom

Romansy 14 ◽  
2002 ◽  
pp. 507-515 ◽  
Author(s):  
Klaus Zimmermann ◽  
Igor Zeidis ◽  
Joachim Steigenberger
Keyword(s):  
Mathematical Model ◽  
Degree Of Freedom ◽  
Infinite Degree
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