In the previous chapters we learned how to analyze the kinematic characteristics of a given mechanism. We were given the design of a mechanism, and we studied ways to determine its mobility, its posture, its velocity, and its acceleration, and we even discussed its suitability for given types of tasks. However, we have said little about how the mechanism is designed – that is, how the sizes and shapes of the links are chosen by the designer.

In our studies of kinematic analysis in the previous chapters, we limited ourselves to consideration of the geometry of the motions and of the relationships between displacement and time. The forces required to produce those motions or the motion that would result from the application of a given set of forces were not considered. We are now ready for a study of the dynamics of machines and systems. Such a study is usually simplified by starting with the statics of such systems.

Just as force is a ubiquitous concept in linear mechanics, torque is ubiquitous in rotational mechanics. We, therefore, begin this chapter with the definition and detailed description of torque, which we then use to study static equilibrium. Our discussion includes descriptions of common forces and their points of application, as well as subtleties associated with studying systems of objects in static equilibrium. The chapter ends with some useful theorems commonly found in the literature.

In this chapter we describe power electronics andpresent a brief introduction to semiconductorswitching devices and magnetic components. Anintroduction to these circuit elements is necessarybecause we use them in Part I, although we do notdiscuss them in detail until Part III. We alsointroduce in this chapter nomenclature that we usethroughout the book.

The brain is the mediator of every aspect of intelligence. Of the many mysteries locked inside human brains, solving how intelligence works may have the most far-reaching consequences. In the short term, knowing how the brain creates intelligence from genetic and nongenetic influences may redefine intelligence in terms of quantifiable brain characteristics and provide brain-based ways to assess individual differences in intelligence. In the longer term, if we learn how to tinker with brain mechanisms to increase reasoning ability, we might enter a new phase of personal achievement and societal well-being. Such knowledge might even create more geniuses on the level of Einstein, Newton, Cervantes, or Da Vinci. Increasing intelligence could even raise the bar for artificial intelligence to catch up to humans (Hawkins, 2021).

The large majority of mechanisms in use today have planar motion, that is, the motions of all points produce paths that lie in a single plane or in parallel planes. This means that all motions can be seen in true size and shape from a single viewing direction and that graphic methods of analysis require only a single view. If the coordinate system is chosen with the x and y axes parallel to the plane(s) of motion, then all z values remain constant, and the problem can be solved, either graphically or analytically, with only two-dimensional methods. Although this is usually the case, it is not a necessity. Mechanisms having three-dimensional point paths do exist and are called spatial mechanisms. Another special category, called spherical mechanisms, have point paths that lie on concentric spherical surfaces.

The most general motion of a rigid body can be described by the combination of the translational motion of its center of mass and the rotational motion of all points of the body about an axis through the center of mass. In this chapter, we apply kinematics, dynamics, and conservation laws to investigate rolling motion, which is a special case of this most general motion. This chapter represents the culmination of all the topics we cover in the first six chapters of this book.

An unfortunate consequence of our preoccupationwith things electrical is that the problems ofheat sinking and thermal management are frequentlyignored until forced on us by sound, sight, orsmell. The insatiable need to make things smaller– and the possibility of doing so by using higherfrequencies and new components and materials –aggravates the problem of heat transfer, becausesuch improvements in power densities are seldomaccompanied by corresponding improvements inefficiency. Thus we are stuck with the task ofgetting the same heat out of a smaller volumewhile disallowing any increase in temperature.

Gears are machine elements used to transmit rotary motion between two shafts, usually with a constant speed ratio. In this chapter, we will discuss the case where the axes of the two shafts are parallel, and the teeth are straight and parallel to the axes of rotation of the shafts; such gears are called spur gears.

The topics we have addressed so far – powercircuits, control, and components – do not coverall the issues encountered in designing a powerelectronic system. Among those we have deferredare: (i) providing gate and base drives to thepower semiconductor switches; (ii) using forcedcommutation to turn off SCRs; (iii) controllingthe transient voltages and currents that accompanyswitching in practical circuits; (iv) contendingwith EMI created by fast switching waveforms; and(v) providing a thermal environment that allowssystem components to operate within theirtemperature ratings. We address these five topicsin Part IV.

Magnetic components such as inductors andtransformers are present in the vast majority ofpower electronic circuits. Inductors store energyin the conversion process, filter switching ripple(as part of input and output filters, forexample), create sinusoidal variations of voltageor current (paired with capacitors, as in resonantconverters), limit the rate of change of current(as in snubber circuits), and limit transientcurrent.