之所以起始於『零』，代前言也。玩過『GoPiGo』者或知要它走『台步』依『規矩』困難乎？更不要說能仿效『小海龜』運動呀！由於涉及許多『物理概念』難講矣！！故歸之於『零』，假裝讀者『自明』哩？？
Rolling resistance
Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body (such as a ball, tire, or wheel) rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy needed for deformation (or movement) of the wheel, roadbed, etc. is recovered when the pressure is removed. Two forms of this are hysteresis losses (see below), and permanent (plastic) deformation of the object or the surface (e.g. soil). Another cause of rolling resistance lies in the slippage between the wheel and the surface, which dissipates energy. Note that only the last of these effects involves friction, therefore the name “rolling friction” is to an extent a misnomer.
In analogy with sliding friction, rolling resistance is often expressed as a coefficient times the normal force. This coefficient of rolling resistance is generally much smaller than the coefficient of sliding friction.[1]
Any coasting wheeled vehicle will gradually slow down due to rolling resistance including that of the bearings, but a train car with steel wheels running on steel rails will roll farther than a bus of the same mass with rubber tires running on tarmac. Factors that contribute to rolling resistance are the (amount of) deformation of the wheels, the deformation of the roadbed surface, and movement below the surface. Additional contributing factors include wheel diameter, speed,[2] load on wheel, surface adhesion, sliding, and relative micro-sliding between the surfaces of contact. The losses due to hysteresis also depend strongly on the material properties of the wheel or tire and the surface. For example, a rubber tire will have higher rolling resistance on a paved road than a steel railroad wheel on a steel rail. Also, sand on the ground will give more rolling resistance than concrete.
Figure 1 Hard wheel rolling on and deforming a soft surface, resulting in the reaction force R from the surface having a component that opposes the motion. (W is some vertical load on the axle, F is some towing force applied to the axle, r is the wheel radius, and both friction with the ground and friction at the axle are assumed to be negligible and so are not shown. The wheel is rolling to the left at constant speed.) Note that R is the resultant force from non-uniform pressure at the wheel-roadbed contact surface. This pressure is greater towards the front of the wheel due to hysteresis.
Primary cause
Asymmetrical pressure distribution between rolling cylinders due to viscoelastic material behavior (rolling to the right).[3]
The primary cause of pneumatic tire rolling resistance is hysteresis:[4]
A characteristic of a deformable material such that the energy of deformation is greater than the energy of recovery. The rubber compound in a tire exhibits hysteresis. As the tire rotates under the weight of the vehicle, it experiences repeated cycles of deformation and recovery, and it dissipates the hysteresis energy loss as heat. Hysteresis is the main cause of energy loss associated with rolling resistance and is attributed to the viscoelastic characteristics of the rubber.
- — National Academy of Sciences[5]
This main principle is illustrated in the figure of the rolling cylinders. If two equal cylinders are pressed together then the contact surface is flat. In the absence of surface friction, contact stresses are normal (i.e. perpendicular) to the contact surface. Consider a particle that enters the contact area at the right side, travels through the contact patch and leaves at the left side. Initially its vertical deformation is increasing, which is resisted by the hysteresis effect. Therefore, an additional pressure is generated to avoid interpenetration of the two surfaces. Later its vertical deformation is decreasing. This is again resisted by the hysteresis effect. In this case this decreases the pressure that is needed to keep the two bodies separate.
The resulting pressure distribution is asymmetrical and is shifted to the right. The line of action of the (aggregate) vertical force no longer passes through the centers of the cylinders. This means that a moment occurs that tends to retard the rolling motion.
Materials that have a large hysteresis effect, such as rubber, which bounce back slowly, exhibit more rolling resistance than materials with a small hysteresis effect that bounce back more quickly and more completely, such as steel or silica. Low rolling resistance tires typically incorporate silica in place of carbon black in their tread compounds to reduce low-frequency hysteresis without compromising traction.[6] Note that railroads also have hysteresis in the roadbed structure.[7]
並非作者不願說呦，跨領域越科系，難言專業啊★
Straight line mechanism
In the late seventeenth century, before the development of the planer and the milling machine, it was extremely difficult to machine straight, flat surfaces. For this reason, good prismatic pairs without backlash were not easy to make. During that era, much thought was given to the problem of attaining a straight-line motion as a part of the coupler curve of a linkage having only revolute connection. Probably the best-known result of this search is the straight line mechanism development by Watt for guiding the piston of early steam engines. Although it does not generate an exact straight line, a good approximation is achieved over a considerable distance of travel.
Peaucellier–Lipkin linkage:
bars of identical colour are of equal length
A Sarrus linkage
Roberts linkage
退而只講如何輔助『小汽車』之『直線運動』︰
Linear motion
Linear motion (also called rectilinear motion[1]) is a motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion with constant velocity or zero acceleration; non uniform linear motion with variable velocity or non-zero acceleration. The motion of a particle (a point-like object) along a line can be described by its position 
Linear motion is the most basic of all motion. According to Newton’s first law of motion, objects that do not experience any net force will continue to move in a straight line with a constant velocity until they are subjected to a net force. Under everyday circumstances, external forces such as gravity and friction can cause an object to change the direction of its motion, so that its motion cannot be described as linear.[3]
One may compare linear motion to general motion. In general motion, a particle’s position and velocity are described by vectors, which have a magnitude and direction. In linear motion, the directions of all the vectors describing the system are equal and constant which means the objects move along the same axis and do not change direction. The analysis of such systems may therefore be simplified by neglecting the direction components of the vectors involved and dealing only with the magnitude.[2]
Neglecting the rotation and other motions of the Earth, an example of linear motion is the ball thrown straight up and falling back straight down.
，避免複雜的『動力學』︰
Analytical dynamics
In classical mechanics, analytical dynamics, or more briefly dynamics, is concerned with the relationship between motion of bodies and its causes, namely the forces acting on the bodies and the properties of the bodies (particularly mass and moment of inertia). The foundation of modern-day dynamics is Newtonian mechanics and its reformulation as Lagrangian mechanics and Hamiltonian mechanics.[1][2]
History
The field has a long and important history, as remarked by Hamilton: “The theoretical development of the laws of motion of bodies is a problem of such interest and importance that it has engaged the attention of all the eminent mathematicians since the invention of the dynamics as a mathematical science by Galileo, and especially since the wonderful extension which was given to that science by Newton.” William Rowan Hamilton, 1834 (Transcribed in Classical Mechanics by J.R. Taylor, p. 237[3])
Some authors (for example, Taylor (2005)[3] and Greenwood (1997)[4]) include special relativity within classical dynamics.
Relationship to statics, kinetics, and kinematics
Historically, there were three branches of classical mechanics:
- “statics” (the study of equilibrium and its relation to forces)
- “kinetics” (the study of motion and its relation to forces).[5]
- “kinematics” (dealing with the implications of observed motions without regard for circumstances causing them).[6]
These three subjects have been connected to dynamics in several ways. One approach combined statics and kinetics under the name dynamics, which became the branch dealing with determination of the motion of bodies resulting from the action of specified forces;[7] another approach separated statics, and combined kinetics and kinematics under the rubric dynamics.[8][9] This approach is common in engineering books on mechanics, and is still in widespread use among mechanicians.
Fundamental importance in engineering, diminishing emphasis in physics
Today, dynamics and kinematics continue to be considered the two pillars of classical mechanics. Dynamics is still included in mechanical, aerospace, and other engineering curricula because of its importance in machine design, the design of land, sea, air and space vehicles and other applications. However, few modern physicists concern themselves with an independent treatment of “dynamics” or “kinematics,” nevermind “statics” or “kinetics.” Instead, the entire undifferentiated subject is referred to as classical mechanics. In fact, many undergraduate and graduate text books since mid-20th century on “classical mechanics” lack chapters titled “dynamics” or “kinematics.”[3][10][11][12][13][14][15][16][17] In these books, although the word “dynamics” is used when acceleration is ascribed to a force, the word “kinetics” is never mentioned. However, clear exceptions exist. Prominent examples include The Feynman Lectures on Physics.[18]
- List of Fundamental Dynamics Principles
，且權充朝向目標前進者的『墊腳石』吧☆