Robot Manipulators - Waterloo Maple
The roll, pitch and yaw angles are (in rad): 1.099543058 1.410139396 0.7853981634 The z-y-z angles are (in rad): 1.244011150 0.5663241952. 0.3457940165 (2.2.4.3.6) Coordinate Transformations Fig. 16: Spatial displacement Consider the point in Fig. 16. Its position vector relative to Frame A can be found using
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Nodal and Loop Analysis - Waterloo Maple
www.maplesoft.comThe circuit in figure 2 consists of multiple elements. We can analyze it with KVL. Firgure 2: KVL Analysis of a Circuit The loop analysis of this circuit element is in a clockwise direction. The loop encounters the negative polarity of A, the positive polarity of B and the positive polarity of C if analyzed in a clockwise direction.
Rotation: Moment of Inertia and Torque - Waterloo Maple
www.maplesoft.comTorque and Newton's Second Law for Rotation Torque, also known as the moment of force, is the rotational analog of force. This word originates from the Latin word torquere meaning "to twist". In the same way that a force is necessary to change a particle or object's state of motion, a torque is necessary to change
Coupled Inductors
www.maplesoft.comFigure 1: Two coils are magnetically coupled, wound around a magnetic core. With coupled inductors, such as those shown in figure 1, two wires are wrapped around a magnetic core. In this diagram, note that the two wires are wrapped around the core in opposite directions and produce the same polarity of voltage. This is due to Lenz's law. A
PID Control - Waterloo Maple
www.maplesoft.cominput and have control over the response characteristics. Once again, similar to the case of P control for a second order system, since all the response specifications depend on the controller gain , it is not possible to control them independently. For example, it is not possible to reduce the rise time and maximum overshoot simultaneously.
Response to Harmonic Excitation - Waterloo Maple
www.maplesoft.comHarmonic excitation refers to a sinusoidal external force of a certain frequency applied to a system. The response of a system to harmonic excitation is a very important topic because it is encountered very commonly and also covers the concept of resonance. Resonance occurs
Transfer Functions, Poles and Zeros - Waterloo Maple
www.maplesoft.comThe step response of the transfer function can be written as This can be expanded to get The first term on the RHS is an impulse response and second term is a step response. Unit impulse response plots for some different cases
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