Example 5.01:: Screw Coordinates (MATLAB)

This example illustrates how to determine a screw's coordinates at three different points.

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The Screw's Pitch $h_{1}$
For Point $P_{A} (0, 3, 0)$
For Point $P_{B} (0, 0, -2)$
For Point $P_{C} (-1, -2, 3)$

Clear All Workspace Objects and Reset All Assumptions

%clear all

The Screw's Pitch $h_{1}$

h1 = 2; % cm

For Point $P_{A} (0, 3, 0)$

S1Res0 = [0; 0; 1]; % [unitless]
XARel0Res0 = [0; 3; 0]; % [cm]
SO1ARes0 = h1*S1Res0 + cross(S1Res0, XARel0Res0); % [cm]
Screw1ARes0 = [S1Res0; SO1ARes0]; % [unitless; cm]

For Point $P_{B} (0, 0, -2)$

XBRel0Res0 = [0; 0; -2]; % [cm]
SO1BRes0 = h1*S1Res0 + cross(S1Res0, XBRel0Res0); % [cm]
Screw1BRes0 = [S1Res0; SO1BRes0]; % [unitless; cm]

For Point $P_{C} (-1, -2, 3)$

XCRel0Res0 = [-1; -2; 3]; % [cm]
SO1CRes0 = h1*S1Res0 + cross(S1Res0, XCRel0Res0); % [cm]
Screw1CRes0 = [S1Res0; SO1CRes0]; % [unitless; cm]

This MATLAB example illustrates a computation from the textbook Fundamentals of Robot Mechanics by G. L. Long, Quintus-Hyperion Press, 2015. See http://www.RobotMechanicsControl.info for additional relevant files.

Example 5.01:: Screw Coordinates (MATLAB)

Contents

Clear All Workspace Objects and Reset All Assumptions

The Screw's Pitch

For Point

For Point

For Point

The Screw's Pitch $h_{1}$

For Point $P_{A} (0, 3, 0)$

For Point $P_{B} (0, 0, -2)$

For Point $P_{C} (-1, -2, 3)$