MIT2_017JF09_p14

MIT2_017JF09_p14 - 14 PENDULUM DYNAMICS AND LINEARIZATION...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
± 14 PENDULUM DYNAMICS AND LINEARIZATION 35 14 Pendulum Dynamics and Linearization Consider a single-link arm, with length l and all the mass m concentrated at the end. A motor at the fixed pivot point supplies a controllable torque τ . As drawn, a positive torque drives the arm counter-clockwise, so as to drive the arm angle θ positive. The arm is free to swing around the full 360 degrees; gravity pulls the arm downward. There is no damping. T l m W g 1. Derive and state the equation of motion for this system. Solution: It is a basic rotary moment of inertia with a gravity effect and input torque. We will get ml 2 θ ¨ = τ mgl cos θ. 2. For each of the linearization angles [-90,0,90] degrees, answer the following: (a) What is the static torque needed to support the arm in this configuration? Solution: the three angles given, the static torque is the amount needed to just balance the gravity torque. These values are [0, mgl , 0]; note that the upward and downward configurations do not take any static torque to maintain.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

MIT2_017JF09_p14 - 14 PENDULUM DYNAMICS AND LINEARIZATION...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online