# OSU ECE 5463 - Manipulator Dynamics-1 (8 pages)

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## Manipulator Dynamics-1

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- Pages:
- 8
- School:
- Ohio State University
- Course:
- Ece 5463 - Introduction to Real Time Robotics Systems

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Manipulator Dynamics 1 Read Chapter 6 What is dynamics Study the force torque required to cause the motion of robots just like engine power required to drive a automobile Most familiar formula f ma f force m mass and a acceleration Manipulator will be more complicated since each link can move and rotate not just a point mass f Acceleration of a rigid body is we need to calculate manipulator dynamics 1 linear acceleration Linear velocity of a vector P in frame B can be expressed in frame A as B A Because Acceleration can be expressed as 2 When the origin of B is moving 2 B Complicated due to a rigid body and b both translational and rotational motions of B and P Acceleration of a rigid body 2 angular acceleration If there are three frames A B and C one may have Then we obtain by taking the derivative of both sides with respect to time which turns out to be Angular acceleration in one frame can be expressed in another frame in an iterative way but could be complicated That will be used in calculating manipulator dynamics 3 Mass distribution For rigid body we have to consider both mass and moment of inertia since a rigid body is free to move in the space with translational and rotational motions Different configurations need different torques to achieve accelerations consider 1 below 1 Ze Xe D1 Z1 X1 Z2 D0 Z0 X2 D2 X0 The moment of inertia is related to the mass distribution of the links and its motions in particular coordinate frames Inertia tensor Using inertia to describe mass distribution with respect to a coordinate Inertia tensor in A can be expressed as distance mass are called mass moments of inertia are called mass products of inertia dv dv dv i j x y or z i j is the density of the material If we chose the frame in such a way that the products of inertias are all zero the axes are called principal axes and mass moments are called the principal moments of inertia dv Inertia tensor examples 1 Which one has greater or Calculate the inertia tensor for the following object and the attached frame Assuming density to be even Inertia tensor examples 2 dxdydz wdydz wdz hw lw l 4h What if we remove the frame to a new place as shown below How can we make the mass products of inertia all zero dxdydz

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