## Characterization of manipulator geometry |

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### Contents

MATHEMATICAL MODEL OF A MECHANICAL MANIPULATOR | 11 |

POSITIONING ACCURACY OF A MECHANICAL MANIPULATOR | 20 |

THE WORKSPACES OF A MECHANICAL MANIPULATOR | 93 |

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### Common terms and phrases

20 CONTINUE algorithm automatic manipulators bounds the reachable calculate the joint CALL contours corresponding curve degree of freedom desired position Dexterous Workspace dextrous workspace different workspaces DIMENSION direction ellipsoid error in positioning fixed frame force applied frame of reference freedom manipulator given grid point Hence hyperboloid joint angles joint axes joint positioning errors joint variables manipulator geometry manipulator hand Manipulator in Example matrix mechanical manipulator normally distributed orientation error orienting the hand partial derivatives planar manipulator position analysis position vector positioning accuracy positioning and orienting positioning the hand positioning the joints principal variances prismatic joint probability of positioning problem random variables reachable workspace reference point RETURN END SUBROUTINE revolute joints screw axis set of equations sets of joint seven equations shown in Figure singular position small displacement solution branch specified probability sphere of radius surface which bounds Udine unit vector values wrench axis zero pitch screw