2012-1807. kinematics robot manipulators
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Introduction
Kinematics of Robot Manipulator1The City College of New York1Examples of Kinematics CalculationsForward kinematics
Given joint variables
End-effector position and orientation, -Formula?
The City College of New York2Examples of Inverse KinematicsInverse kinematicsEnd effector position and orientation
Joint variables -Formula?3
The City College of New York3Example 1: one rotational link4
The City College of New York4Robot Reference FramesWorld frameJoint frameTool frame5
WRPTThe City College of New York5WF is a universal coordinate frame.
JF is used to specify movements of each individual joint of the robot.
HF specifies movements of the robots hand relative to a frame attached to the handCoordinate TransformationReference coordinate frame OXYZBody-attached frame Ouvw
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O, OPoint represented in OXYZ:
Point represented in Ouvw:Two frames coincide ==>The City College of New York6Properties: Dot ProductMutually perpendicular
Unit vectors7Properties of orthonormal coordinate frame
Let and be arbitrary vectors in and be the angle from to , then
The City College of New York7Coordinate TransformationCoordinate TransformationRotation only
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How to relate the coordinate in these two frames?
The City College of New York8Basic RotationBasic Rotation , , and represent the projections of onto OX, OY, OZ axes, respectively
Since
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The City College of New York9Basic Rotation MatrixBasic Rotation Matrix
Rotation about x-axis with
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The City College of New York10Is it True? Can we check? Rotation about x axis with
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The City College of New York11Basic Rotation MatricesRotation about x-axis with
Rotation about y-axis with
Rotation about z-axis with
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The City College of New York12Matrix notation for rotationsBasic Rotation Matrix
Obtain the coordinate of from the coordinate of
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