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# chapter2 - Introduction to Robotics H Harry Asada 1 Chapter...

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Introduction to Robotics, H. Harry Asada 1 Chapter 2 Actuators and Drive Systems Actuators are one of the key components contained in a robotic system. A robot has many degrees of freedom, each of which is a servoed joint generating desired motion. We begin with basic actuator characteristics and drive amplifiers to understand behavior of servoed joints. Most of today’s robotic systems are powered by electric servomotors. Therefore, we focus on electromechanical actuators. 2.1 DC Motors Figure 2-1 illustrates the construction of a DC servomotor, consisting of a stator, a rotor, and a commutation mechanism. The stator consists of permanent magnets, creating a magnetic field in the air gap between the rotor and the stator. The rotor has several windings arranged symmetrically around the motor shaft. An electric current applied to the motor is delivered to individual windings through the brush-commutation mechanism, as shown in the figure. As the rotor rotates the polarity of the current flowing to the individual windings is altered. This allows the rotor to rotate continually. Figure 2.1.1 Construction of DC motor Let m τ be the torque created at the air gap, and i the current flowing to the rotor windings. The torque is in general proportional to the current, and is given by i K t m = ( 2 . 1 . 1 ) where the proportionality constant is called the torque constant , one of the key parameters describing the characteristics of a DC motor. The torque constant is determined by the strength of the magnetic field, the number of turns of the windings, the effective area of the air gap, the radius of the rotor, and other parameters associated with materials properties. t K In an attempt to derive other characteristics of a DC motor, let us first consider an idealized energy transducer having no power loss in converting electric power into mechanical Department of Mechanical Engineering Massachusetts Institute of Technology Angle θ Stator Winding Bearings Shaft Brush i a N Commutator S Inertia Load Figure by MIT OCW.

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Introduction to Robotics, H. Harry Asada 2 power. Let E be the voltage applied to the idealized transducer. The electric power is then given by , which must be equivalent to the mechanical power: i E m m in i E P ω τ = = ( 2 . 1 . 2 ) where m is the angular velocity of the motor rotor. Substituting eq.(1) into eq.(2) and dividing both sides by i yield the second fundamental relationship of a DC motor: m t K E = ( 2 . 1 . 3 ) The above expression dictates that the voltage across the idealized power transducer is proportional to the angular velocity and that the proportionality constant is the same as the torque constant given by eq.(1). This voltage E is called the back emf (electro-motive force) generated at the air gap, and the proportionality constant is often called the back emf constant.
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chapter2 - Introduction to Robotics H Harry Asada 1 Chapter...

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