In this chapter we introduce polyphase systems,their advantages relative to single-phase systems,and how they are represented. We then use thesingle-phase bridge circuit as a building block tocreate polyphase rectifiers and inverters. We alsodiscuss the operating characteristics of thesecircuits from both the ac and dc sides.

Psychometric models do not explain the processes that underlie thinking. They are not intended to do so, but they nevertheless contribute to understanding intelligence. This has been the case since at least 1923, when Charles Spearman wrote The Nature of Intelligence and the Principles of Cognition. As Sternberg (2016, p. 236) highlighted, “Spearman believed that apprehension of experience, education of relations, and education of correlates are the basic overlapping information processes of intelligence. … The great psychometricians of all time – Spearman and Carroll – were also astute cognitive psychologists.”

When a power semiconductor switch is either onor off, its power dissipation is relatively small.However, the transition from one state to theother is often not so benign, and can imposesimultaneous high voltage and high current on theswitching device. Special efforts are oftenrequired to ensure that the device will survivethis most stressful part of its operating cycle.We have already seen in Fig. 22.4(b) how a snubbercircuit consisting of$C_s$ and$R_s$ can moderatethe effects of parasitic inductance.

The first eight chapters of this book focused on individual differences in intelligence. In Chapter 1, we introduced issues about group comparisons (Box 1.2) and some of the sensitive issues surrounding them. Before we discuss findings about sex (Chapter 10), age (Chapter 11), and differences around the world (Chapter 12), this chapter describes and discusses a number of essential issues required for properly interpreting data at the group or population level.

The phase-controlled dc/ac converter introducedin Chapter 4 requires that the external ac systembe a voltage source, typically the ac utilityline. This condition is necessary because thephase-controlled converter uses the reversal ofthe ac voltage to drive the commutation process.Therefore the ac frequency in these circuits isconstrained to be that of the ac source. In thischapter we remove the restriction that the acsystem be a voltage source, realizing that bydoing so we must use means other than linecommutation to turn devices off. These circuits,which we call switched-modedc/ac converters, use fully controllabledevices such as MOSFETs and IGBTs, and switch atfrequencies that are higher (often much higher)than the ac-side frequency.

In Chapters 2, 3, and 4, we concentrated entirely on problems that exhibit a single degree of freedom, and can be analyzed by specifying the motion of a single input variable. This was justifiable, since, by far, the vast majority of practical mechanisms are designed to have only one degree of freedom so that they can be driven by a single power source. However, there are mechanisms that have multiple degrees of freedom and can only be analyzed if more than one input motion is given. In this chapter, we will look at how our methods can be used to find the positions, velocities, and accelerations of these mechanisms.

Since velocity is a vector quantity, the change in velocity, Δ𝐕P, and the acceleration, 𝐀P, are also vector quantities – that is, they have both magnitude and direction. Also, like velocity, the acceleration vector is properly defined only for a point; the term should not be applied to a line, a coordinate system, a volume, or any other collection of points, since the accelerations of different points may be different.

Ancestry and country differences in intelligence test scores are a matter of heated discussion. This chapter addresses delicate issues. Even when the data are relatively clear, discussion about their interpretation and meaning easily slips into dispute. We wrote this chapter to shed light and insight instead of lightning and thunder. Our focus is the world because the issues are significant across the globe (Hunt, 2012; Jones, 2016; Rindermann, 2018). To maintain the global focus, we are not detailing data within the United States beyond what is summarized in Box 12.1. As we do throughout this book, we emphasize key research because we agree with James Flynn’s (2018, p. 128) view on this subject: “There will be bad science on both sides of the debate. The only antidote I know for that is to use the scientific method as scrupulously as possible.”

In this chapter, we begin by examining the work due to a torque. We then define the concept of the rotational kinetic energy for a point mass, systems of discrete masses, and continuous rigid bodies. We develop the angular work-kinetic energy theorem and use it to study the conservation of energy and the conservation of mechanical energy in systems involving rotational motion. To develop these theorems, we draw from our understanding of the analogous theorems in linear motion.

Pulse-width-modulated switching converters arepower circuits in which the semiconductor devicesswitch between on and off states at a rate that isfast compared to the frequencies of the input andoutput waveforms. Control of the converter isexercised by varying the ratio of on-time to totalswitching period of the controlling switches,thereby controlling the width of the pulsesapplied to the output. This is called pulse-width modulation orPWM control.

A basic understanding of device physics, andhow the physics relates to device behavior, arevaluable assets for both interpreting a device’sspecification and its successful application.

A power circuit is typically composed of only afew kinds of components (other than its source andload): switches, and energy storage elements suchas capacitors and inductors (or transformers). Inits ideal form, each of these components islossless and capable of operating at anyfrequency. In the ideal switch, for instance, thevoltage across it is zero when it is on, thecurrent flowing through it is zero when it is off,and the transition between these two states occursinfinitely fast. Although we did not explicitlydiscuss the means by which the actual switches areturned on and off (a topic covered in Chapter 23),an ideal switch responds infinitely fast to itsdrive signal and requires zero drive power.

The rectifier circuits discussed so far areuncontrollable; that is, their output voltage is afunction of system parameters and cannot beadjusted in response to parametric changes, suchas variations in load$(I_d)$ or ac voltage$(V_s)$.

The purpose of this chapter is to apply fundamentals – kinematic and dynamic analysis – in a complete investigation of a particular class of machines. The reciprocating engine has been selected for this purpose, since it has reached a high state of development and is of more general interest than most other machines. For our purposes, however, another type of machine involving interesting dynamic situations would serve just as well. The primary objective of the chapter is to demonstrate methods of applying fundamentals to the dynamic analysis of machines.

When rotational motion is to be transmitted between parallel shafts, engineers often prefer to use spur gears, since they are easy to design and very economical to manufacture. However, sometimes the design requirements are such that helical gears are a better choice. This is especially true when the loads are heavy, the speeds are high, or the noise level must be kept low.