Influence of Frame Stiffness and Rider Position on Bike Dynamics: Analytical Study

2015 ◽  
Author(s):  
Trevor Williams ◽  
Sudhir Kaul ◽  
Anoop Dhingra
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Critical Role ◽  
Rear Wheel ◽  
Front Wheel ◽  
Rigid Bodies ◽  
Limited Attention ◽  
Structural Stiffness ◽  
Bicycle Frame

Dynamic characteristics of a bicycle such as handling and stability can be studied during the design phase to comprehend specific aspects associated with the overall layout as well as the frame architecture. Bicycles demonstrate unique properties such as static instability that is overcome by getting them into motion with a minimum velocity threshold. The structural stiffness of a frame plays a critical role in the handling behavior of a bike. However, the influence of structural stiffness has received limited attention in the existing literature. This paper attempts to fill the gap by presenting analytical results from a study that includes the influence of rider positions on three bicycle layouts. The analytical model consists of four rigid bodies: rear frame, front frame (front fork and handle bar assembly), front wheel and rear wheel. The overall model exhibits three degrees-of-freedom: the roll angle of the frame, the steering of the front frame, and the rotation of the rear wheel with respect to the frame. The rear frame is divided into two parts, the rider and the bicycle frame, that are assumed to be rigidly connected. This is done in order to allow the model to account for varying rider positions. The influence of frame flexibility is studied by coupling the structural stiffness of the frame to the governing equations of motion. Layouts from a benchmark bicycle, a commercially manufactured bicycle, and a cargo bicycle are used for this study in conjunction with rider positions ranging from a relaxed position to an extreme prone position. All the results are analyzed and compared with some proven analytical and experimental results in the existing literature. Results indicate that some of the rider positions can play a significant role in influencing the dynamic characteristics of the bike. Structural stiffness is seen to significantly affect the weave mode, only when the stiffness is reduced substantially.

A Unified Framework for Dynamics and Lyapunov Stability of Holonomically Constrained Rigid Bodies

2005 ◽  
Vol 9 (4) ◽  
pp. 387-394 ◽  
Author(s):  
Khoder Melhem ◽  
◽  
Zhaoheng Liu ◽  
Antonio Loría ◽  
◽  
...  
Keyword(s):  
System Dynamics ◽  
Lyapunov Stability ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Minimal Realization ◽  
State Variables ◽  
Unified Framework ◽  
Constrained System ◽  
And Control

A new dynamic model for interconnected rigid bodies is proposed here. The model formulation makes it possible to treat any physical system with finite number of degrees of freedom in a unified framework. This new model is a nonminimal realization of the system dynamics since it contains more state variables than is needed. A useful discussion shows how the dimension of the state of this model can be reduced by eliminating the redundancy in the equations of motion, thus obtaining the minimal realization of the system dynamics. With this formulation, we can for the first time explicitly determine the equations of the constraints between the elements of the mechanical system corresponding to the interconnected rigid bodies in question. One of the advantages coming with this model is that we can use it to demonstrate that Lyapunov stability and control structure for the constrained system can be deducted by projection in the submanifold of movement from appropriate Lyapunov stability and stabilizing control of the corresponding unconstrained system. This procedure is tested by some simulations using the model of two-link planar robot.

Vehicle Dynamics Model Establishing and Dynamic Characteristic Simulation

2013 ◽  
Vol 404 ◽  
pp. 244-249
Author(s):  
Rui Wang ◽  
Hao Zhang ◽  
Xian Sheng Li ◽  
Xue Lian Zheng ◽  
Yuan Yuan Ren
Keyword(s):  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Rear Wheel ◽  
Front Wheel ◽  
Step Response ◽  
Steering Wheel ◽  
Vehicle Simulation ◽  
Equivalent Mechanical Model ◽  
External Forces ◽  
Three Degrees Of Freedom

By establishing bus simplify coordinate system model and equivalent mechanical model, inertial forces and external forces are analyzed through vehicle lateral movement and vehicle's yaw motion and roll motion. Three degrees of freedom linear motion equation of vehicle is established taking into account lateral motion, yawing movement and rolling motion of vehicle and it can be solved by using method of state space equation. Vehicle dynamic characteristics are analyzed by using this method and programming with Matlab. Vehicle in steering wheel angle step response is analyzed under the conditions of different tire wheel cornering stiffness, moment of inertia, height of center of mass. The results show that increasing rear wheel cornering stiffness, reducing front wheel cornering stiffness and center of mass height, which can effectively improve stability of vehicle. Simulation results provide a theoretical basis and reference for the selection and design of vehicle.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

Modeling Spatial Rigid Multibody Systems Using an Explicit-Time Integration Finite Element Solver and a Penalty Formulation

2004 ◽  
Author(s):  
Tamer Wasfy
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time Integration ◽  
Rigid Bodies ◽  
Rotation Matrix ◽  
Explicit Time Integration ◽  
Penalty Formulation ◽  
A New Technique ◽  
Rigid Multibody

A new technique for modeling rigid bodies undergoing spatial motion using an explicit time-integration finite element code is presented. The key elements of the technique are: (a) use of the total rotation matrix relative to the inertial frame to measure the rotation of the rigid bodies; (b) time-integration of the rotational equations of motion in a body fixed (material) frame, with the resulting incremental rotations added to the total rotation matrix; (c) penalty formulation for creating connection points (virtual nodes which do not add extra degrees of freedom) on the rigid-body where joints can be placed. The use of the rotation matrix along with incremental rotation updates circumvents the problem of singularities associated with other types of three and four parameter rotation measures. Benchmark rigid multibody dynamics problems are solved to demonstrate the accuracy of the present technique.

Divide-and-Conquer Based Adaptive Coarse Grained Simulation of RNA

2010 ◽  
Author(s):  
Mohammad Poursina ◽  
Kishor Bhalerao ◽  
Kurt Anderson
Keyword(s):  
Molecular Modeling ◽  
Degrees Of Freedom ◽  
Traditional Approach ◽  
Equations Of Motion ◽  
Critical Role ◽  
Divide And Conquer ◽  
Coarse Grained ◽  
Biomolecular Systems ◽  
Spatial And Temporal Scales ◽  
O 10

Molecular modeling has gained increasing importance in recent years for predicting important structural properties of large biomolecular systems such as RNA which play a critical role in various biological processes. Given the complexity of biopolymers and their interactions within living organisms, efficient and adaptive multi-scale modeling approaches are necessary if one is to reasonably perform computational studies of interest. These studies nominally involve multiple important physical phenomena occurring at different spatial and temporal scales. These systems are typically characterized by large number of degrees of freedom O(103) – O(107). The temporal domains range from sub-femto seconds (O(10−16)) associated with the small high frequency oscillations of individual tightly bonded atoms to milliseconds (O(10−3)) or greater for the larger scale conformational motion. The traditional approach for molecular modeling involved fully atomistic models which results in fully decoupled equations of motion. The problems with this approach are well documented in literature.

Dynamic Characteristics of an In-Contact Headslider Considering Meniscus Force: Part 1—Formulation and Application to the Disk With Sinusoidal Undulation

1999 ◽  
Vol 122 (3) ◽  
pp. 633-638 ◽  
Author(s):  
Takahisa Kato ◽  
Souta Watanabe ◽  
Hiroshige Matsuoka
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Disk Surface ◽  
Disk Interface ◽  
Meniscus Force ◽  
Calculation Results ◽  
Three Degrees Of Freedom

The authors present a three-degrees-of-freedom (3-DOF) model of an in-contact headslider/disk interface (HDI) system by which the dynamic characteristics of the in-contact headslider-suspension assembly can be obtained. Four regimes with respect to the interface of headslider and disk surface are shown to take the meniscus force of lubricant on the disk surface into account. The equations of motion of the in-contact headslider considering the meniscus force at each regime and the calculation results for the disk with sinusoidal undulation are described. [S0742-4787(00)01802-6]

A Computational Aerodynamic Study of Tandem Rotating Wheels in Contact with the Ground

2018 ◽  
Vol 7 (3.17) ◽  
pp. 133
Author(s):  
Mohammad Rasidi Rasani ◽  
Azhari Shamsudeen ◽  
Zambri Harun ◽  
Wan Mohd Faizal Wan Mahmood
Keyword(s):  
Lift Coefficient ◽  
Rear Wheel ◽  
Front Wheel ◽  
Navier Stokes ◽  
Limited Attention ◽  
Road Vehicles ◽  
Reynolds Average Navier Stokes ◽  
Drag And Lift ◽  
Reynolds Average ◽  
Good Agreement

Wheels have significant impact on noise and drag of road vehicles, which may influence their fuel consumption, emission and comfort. A number of studies have analyzed flow and aerodynamics of isolated wheel in contact with the ground, but limited attention has been given to interaction between wheels. The present study aims to compare the aerodynamics and flow structure between single and tandem wheels. To that end, flow around single and tandem wheels are simulated using a turbulence Scaled Adaptive Unsteady Reynolds Average Navier Stokes (URANS) model. Wheel geometry was based on the actual wheel used in the experiments of Fackrell and Harvey. Flow around single and tandem wheels were examined and compared, along with their respective drag and lift coefficients. Results for single wheel in contact with the ground show good agreement with previous experiments. In the tandem wheel case, the rear wheel exhibits lower drag coefficient (CD = 0.37) and more downforce (lift coefficient CL = -0.14) compared to the front wheel. The present investigation may help to illustrate impact of wheel interaction on their aerodynamics.  

Development of a Servohydraulic Roller Test Bench for Indoor Evaluation of the Vibrational Comfort of Bicycle Components

2015 ◽  
Author(s):  
Nicola Petrone ◽  
Francesco Trabacchin ◽  
Fausto Panizzolo
Keyword(s):  
Test Bench ◽  
Rear Wheel ◽  
Front Wheel ◽  
Random Vibrations ◽  
Bicycle Frame ◽  
Vibration Transmissibility

One of the most important parameters evaluated by racing and trekking cyclists is vibrational comfort: as generally accepted, it is closely correlated to the response of bicycle components in combination with the cyclist’s characteristics. Vibration transmissibility of wheels and saddles was recently studied during lab tests using a wooden dummy bottom resting on the saddle or in road tests on an instrumented racing bicycle at different speeds on different surfaces. The use of shakers is also well established in the evaluation of cyclist’s posture effects on the overall bicycle behaviour. In fact, in previous works, either a servohydraulic actuator was applied to the seatpost of a bicycle frame hinged at the front wheel axle with a cycling tester, or two electrodynamic shakers were applied under the wheels of a fully equipped bicycle, with a cyclist sitting statically on the saddle. In the present study, the combination of a servohydraulic actuator and a roller type bench allowed to overcome the limitations of the former experiences. Random vibrations were input to the bicycle-cyclist complex by means of rollers supporting the rear wheel while cyclists were cycling unrestrained on the rollers. The test bench setup and tuning approach are presented for comparison with results available from previous bench and road tests.

Vibration Modes of Helical Planetary Gears

2009 ◽  
Author(s):  
Tugan Eritenel ◽  
Robert G. Parker
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Lumped Parameter Model ◽  
Vibration Modes ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Modal Properties ◽  
Lumped Parameter

This paper examines the vibration modes of single stage helical planetary gears in three dimensions with equally spaced planets. A lumped-parameter model is formulated to obtain the equations of motion. The gears and shafts are modeled as rigid bodies with compliant bearings at arbitrary axial locations on the shafts. A translational and a tilting stiffness account for the force and moment transmission at the gear mesh interface. The modal properties generalize those of two-dimensional spur planetary gears; there are twice as many degrees of freedom and natural frequencies due to the added tilting and axial motion. All vibration modes are categorized as planet, rotational-axial, and translational-tilting modes. The modal properties are shown to hold even for configurations that are not symmetric about the gear plane, due to, for example, shaft bearings not being equidistant from the gear plane. Computational modal analysis are performed to numerically verify the findings.

Dynamic Analysis of a Motorized Spindle With Externally Pressurized Air Bearings

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Chundong Xu ◽  
Shuyun Jiang
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Forced Response ◽  
Air Bearings ◽  
Motorized Spindle ◽  
Static And Dynamic Characteristics ◽  
Rotating Speed ◽  
Rotor Bearing ◽  
Bearing System

The purpose of this paper is to investigate the dynamic characteristics of a motorized spindle with externally pressurized air bearings. The externally pressurized air bearings consist of a journal bearing and a double pad thrust bearing with orifice restrictors. The equations of motion for the rotor-bearing system are established considering five degrees-of-freedom (DOF). The perturbation method and the finite difference method are introduced to calculate the static and dynamic characteristics of the air bearings; and the effects of the rotating speed and tilt angle of the rotor on the dynamic characteristics of the air bearings are analyzed. With the dynamic coefficients of the air bearings and the 5DOF rotor-dynamic model obtained, the stability, the unbalance response, and the forced response of the rotor-bearing system are investigated. Finally, the static and dynamic characteristics of the spindle are verified by an experimental study.

Sign in / Sign up

Export Citation Format

Share Document