Comparison of the Dynamics of Conventional and Worm-Gear Differentials

1989 ◽  
Vol 111 (4) ◽  
pp. 605-610 ◽  
Author(s):  
J. S. Freeman ◽  
S. A. Velinsky
Keyword(s):  
High Performance ◽  
Equations Of Motion ◽  
Worm Gear ◽  
Road Vehicles ◽  
Bevel Gears ◽  
Full Vehicle ◽  
Lagrange Formulation ◽  
Differential Mechanism ◽  
Interesting Behavior ◽  
Gear Differential

The differential mechanism has been used for many years and a variety of unique designs have been developed for particular applications. This paper investigates the performance of both the conventional bevel-gear differential and the worm-gear differential as used in vehicles. The worm-gear differential is a design in which the bevel gears of the conventional differential are replaced by worm gear/worm wheel pairs. The resultant differential exhibits some interesting behavior which has made this differential desirable for use in high performance and off-road vehicles. In this work, an Euler-Lagrange formulation of the equations of motion of the conventional and worm-gear differentials allows comparison of their respective behavior. Additionally, each differential is incorporated into a full vehicle model to observe their effects on gross vehicle response. The worm-gear differential is shown to exhibit the desirable characteristics of a limited-slip differential while maintaining the conventional differential’s ability to differentiate output shaft speeds at all power levels.

The Design of a Chain of Spherical Stephenson Mechanisms for a Gearless Robotic Pitch-Roll Wrist

2005 ◽  
Vol 128 (2) ◽  
pp. 422-429 ◽  
Author(s):  
S. Hernandez ◽  
S. Bai ◽  
J. Angeles
Keyword(s):  
Unmodeled Dynamics ◽  
Manufacturing Cost ◽  
Interference Avoidance ◽  
Dimensional Synthesis ◽  
Bevel Gears ◽  
Industrial Manipulators ◽  
Differential Mechanism ◽  
Gear Trains ◽  
Robot Performance ◽  
A Chain

Although bevel-gear robotic wrists are widely used in industrial manipulators due to their simple kinematics and low manufacturing cost, their gear trains function under rolling and sliding, the latter bringing about noise and vibration. Sliding is inherent to the straight teeth of the bevel gears of these trains. Moreover, unavoidable backlash introduces unmodeled dynamics, which mars robot performance. To alleviate these drawbacks, a gearless pitch-roll wrist is currently under development for low backlash and high stiffness. The wrist consists of spherical cam-rollers and spherical Stephenson linkages, besides two roller-carrying disks that drive a combination of cams and Stephenson mechanisms, the whole system rotating as a differential mechanism. The paper focuses on the design of the chain of spherical Stephenson mechanisms. The problem of the dimensional synthesis is addressed, and interference avoidance is discussed. An embodiment of the concept is also included.

Differential-Geometric Methods in Multibody Dynamics and Control

2005 ◽  
Author(s):  
P. Maißer
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Multibody System ◽  
Equations Of Motion ◽  
Geometric Approach ◽  
Motion Equations ◽  
Constrained Mechanical Systems ◽  
Dynamics And Control ◽  
Set Up ◽  
Lagrangian Motion

This paper presents a differential-geometric approach to the multibody system dynamics regarded as a point dynamics in a n-dimensional configuration space Rn. This configuration space becomes a Riemannian space Vn the metric of which is defined by the kinetic energy of the multibody system (MBS). Hence, all concepts and statements of the Riemannian geometry can be used to study the dynamics of MBS. One of the key points is to set up the non-linear Lagrangian motion equations of tree-like MBS as well as of constrained mechanical systems, the perturbed equations of motion, and the motion equations of hybrid MBS in a derivative-free manner. Based on this approach transformation properties can be investigated for application in real-time simulation, control theory, Hamilton mechanics, the construction of first integrals, stability etc. Finally, a general Lyapunov-stable force control law for underactuated systems is given that demonstrates the power of the approach in high-performance sports applications.

scholarly journals Study on Small-size Hourglass Worm Gear with a High Performance (4th Report)

2002 ◽  
Vol 2002 (0) ◽  
pp. 135-136
Author(s):  
ZI HE LU ◽  
MINORU MAKI ◽  
TAKAYYUKI SUYAMA ◽  
TAKESHI SAITOH
Keyword(s):  
High Performance ◽  
Worm Gear

scholarly journals Design and calculation of planetary transmission with bevel gears

2019 ◽  
Vol 13 (2) ◽  
pp. 154-161
Author(s):  
Ivan Sabo ◽  
Milan Kljain ◽  
Mirko Karakašić ◽  
Željko Ivandić
Keyword(s):  
Internal Combustion Engine ◽  
Contact Pressure ◽  
Combustion Engine ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Hertz Contact ◽  
Road Vehicles ◽  
Bevel Gears ◽  
Planetary Transmission ◽  
Root Stress

In this paper, the design and calculation of planetary transmission with bevel gears for road vehicles is presented. It must transfer power to the wheels with the possibility that wheels can rotate at different speeds. The basic calculation of transmission is performed for the drive machine, where an internal combustion engine is chosen, and for the driven machine, which is a car, all forces of resistance are calculated so that the transmission needs to be overcome to move the car. Based on the standard ISO 23509:2016 norm, the calculation of geometry is performed for the input gear pair and it is defined as a hypoid gear pair. For the planetary transmission, a calculation of gear module for bevel gears is first performed, and after that, the geometry is calculated. The calculation of the stress for root stress and Hertz contact pressure is performed for all bevel gears in transmission.

scholarly journals Exploring the Dynamics of Base-Excited Structures Impacting a Rigid Stop

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Peter J. Christopher ◽  
Barnaby Dobson ◽  
Nicholas A. Alexander
Keyword(s):  
High Performance ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Performance Measure ◽  
Nonsmooth Dynamics ◽  
Structural Parameter ◽  
Sigmoid Function ◽  
Stiffness Ratio ◽  
Complex Behaviour ◽  
Interstorey Drift

This paper explores the nonlinear dynamics of a multidegree of freedom (MDoF) structure impacting a rigid stop. The contact mechanics is simplified by continuous sigmoid function idealisation of a lossless spring. By introducing a smooth nonlinear formulation, we avoid the computational expense of event-driven, piecewise, nonsmooth dynamics. A large parametric study using high-performance computing is undertaken. The nondimensional equations of motion suggest one primary structural parameter, contact-to-storey stiffness ratio, and two excitation parameters, nondimensional ground amplitude and frequency. Bifurcation plots indicate an extremely rich and complex behaviour, particularly in the cases where at least two-floor degrees of freedom (DoFs) impact the stop and when the contact-to-storey stiffness ratio is large. When considering interstorey drift as a performance measure, period-1 impacting solutions are generally favourable when compared to an analogous nonimpacting case. This paper also discusses whether chaotic impacting can be favourable. Finally, we consider the question of whether higher modes are significantly excited, at a linear resonance, for impacting solutions to this system.

scholarly journals Lorentz Violation at the Level of Undergraduate Classical Mechanics

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1734 ◽  
Author(s):  
Madeline Clyburn ◽  
Charles D. Lane
Keyword(s):  
Classical Limit ◽  
Binary Star ◽  
Equations Of Motion ◽  
Computational Simulation ◽  
Classical Mechanics ◽  
Lorentz Violation ◽  
Standard Model Extension ◽  
Model Extension ◽  
Binary Star System ◽  
Interesting Behavior

In this paper, we use the classical limit of the Standard-Model Extension to explore some generic features of Lorentz violation. This classical limit is formulated at the level of undergraduate physics. We first discuss the general equations of motion and then concentrate on three specific systems. First, we consider the theoretical aspects of pendulum motion in the presence of Lorentz violation, followed by some sample experimental results. The experimental bounds we achieve, in the range of 10−3, are not competitive with the current bounds from atomic clocks; rather, our experiment illustrates some common ideas and methods that appear in Lorentz-violation studies. We then discuss how Newton’s 2nd Law must be treated with caution in our model. Finally, we introduce a computational simulation of a binary star system that is perturbed by Lorentz-violating effects. This simulation shows some interesting behavior that could be the subject of future analytical studies.

Trajectory optimisation of an aerobatic air race

2009 ◽  
Vol 113 (1139) ◽  
pp. 1-8 ◽  
Author(s):  
H. van der Plas ◽  
H. G. Visser
Keyword(s):  
High Performance ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Optimal Solution ◽  
Open Loop ◽  
Receding Horizon ◽  
Mass Model ◽  
Control Approach ◽  
Time Optimal ◽  
Trajectory Optimisation

Abstract This paper deals with the synthesis of optimal trajectories for aerobatic air races. A typical example of an air race event is the Red Bull Air Race World Series, where high-performance aerobatic aircraft fly a prescribed slalom course consisting of specially designed inflatable pylons, known as ‘air gates’, in the fastest possible time. The trajectory that we seek to optimise is based on such a course. The air race problem is formulated as a minimum-time optimal control problem and solved in open-loop form using a direct numerical multi-phase trajectory optimisation approach based on collocation and non-linear programming. The multiphase feature of the employed collocation algorithm is used to enable a Receding-Horizon optimisation approach, in which only a limited number of manoeuvres in sequence is considered. It is shown that the Receding-Horizon control approach provides a near-optimal solution at a significantly reduced computational cost relative to trajectory optimisation over the entire course. To avoid the path inclination singularity in the equations of motion based on Euler angles, a point-mass model formulation is used that is based on quaternions. Numerical results are presented for an Extra 300S, a purpose-designed aerobatic aircraft.

scholarly journals An Euler–Lagrange approach for studying blood flow in an aneurysmal geometry

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160774 ◽  
Author(s):  
M. A. Xenos
Keyword(s):  
Blood Flow ◽  
Equations Of Motion ◽  
Curvilinear Coordinates ◽  
Solution Approach ◽  
Moving Wall ◽  
Lagrange Formulation ◽  
Euler Form ◽  
Aneurysmal Neck ◽  
Flow Vortex ◽  
Volume Method

To numerically study blood flow in an aneurysm, the development of an approach that tracks the moving tissue and accounts for its interaction with the fluid is required. This study presents a mathematical approach that expands fluid mechanics principles, taking into consideration the domain’s motion. The initial fluid equations, derived in Euler form, are expanded to a mixed Euler–Lagrange formulation to study blood flow in the aneurysm during the cardiac cycle. Transport equations are transformed into a moving body-fitted reference frame using generalized curvilinear coordinates. The equations of motion consist of a coupled and nonlinear system of partial differential equations (PDEs). The PDEs are discretized using the finite volume method. Owing to strong coupling and nonlinear terms, a simultaneous solution approach is applied. The results show that velocity is substantially influenced by the pulsating wall. Intensification of polymorphic flow patterns is observed. Increments of Reynolds and Womersley numbers are evident as pulsatility increases. The pressure field reveals areas of a lateral pressure gradient at the aneurysm. As pulsatility increases, the diastolic flow vortex shifts towards the aortic wall, distal to the aneurysmal neck. Wall shear stress is amplified at the shoulders of the moving wall compared with that of the rigid one.

Simulation Study on CMM Measuring Path Based on the CAD Models of Bevel Gear

2012 ◽  
Vol 591-593 ◽  
pp. 615-619
Author(s):  
Xiao Bao Zhang ◽  
Hong Xia Shi ◽  
Ning Liu ◽  
Xian Jiang Zhou
Keyword(s):  
Simulation Study ◽  
Bevel Gear ◽  
Cnc Machining ◽  
Variable Ratio ◽  
Compact Structure ◽  
Bevel Gears ◽  
Cad Models ◽  
Processing Accuracy ◽  
In Transit ◽  
Gear Differential

As an important part in sliding-limiting differential, the variable ratio noncircular bevel gears can increase the locking factor of the bevel gear differential and improve the vehicles’ off-road capability in transit. At present, this differential has become a study hotspot that many researchers are working over because of its compact structure, cheap cost, good assembly and perdurable capability. In order to get the bevel gear’s processing accuracy, this paper introduced the generating process of the bevel gear’s CMM measuring path, probed the similarity in motion between spherical cutter’s CNC machining and CMM measuring, and then simulated and analyzed the bevel gear’s CMM measuring path by power mill in use of NC authentication method, which provided a reference for the choice of complex surfaces’ measuring methods.

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