HW7_08S - M receives a force from the spring ) ( 2 θ-× =...

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University of California at Berkeley Department of Mechanical Engineering ME132 Dynamic Systems and Feedback Spring 2008 Homework Set #7 Assigned: April 15 (Tu) Due: April 24 (Th) [1] Sketched below is the schematic diagram of a precision positioning system. The drive shaft is driven by the torque input, ) ( t in τ . J represents the moent of inertia of the drive shaft and other moving parts on the drive side. s k the compliance of the shaft. The rotational motion of the shaft is transfored to linear motion by a ball screw. The table mass represented by
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Unformatted text preview: M receives a force from the spring ) ( 2 θ-× = J s s k r f . The mass of the positioning table is represented by M . The table is sliding on a linear guide, and the friction between the table and the linear guide satisfies bv f g = . Use the angular velocity and position of the inertia ( J ) and the velocity and position of the mass ( M ) as state variables and derive the equations of motion. [2] 23.5-5 k s Friction M J τ in (t) ϖ J (t) θ (t) ϖ 2 (t)=r × v(t) θ (t)=r × x(t v(t), x(t) bv(t)...
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This note was uploaded on 08/01/2008 for the course ME 132 taught by Professor Tomizuka during the Spring '08 term at University of California, Berkeley.

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