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Introduction to Robotics cpsc - 460. Lecture 2A – DH Notation. Textbook. Robotics, Vision and Control - Fundamental Algorithms in MATLAB, Peter Corke , Springer, 2011 Author: Peter Corke Publisher: Springer ISBN: 978-3-642-20144-8. Kinematics.
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Introduction to Roboticscpsc - 460 Lecture 2A – DH Notation
Textbook Robotics, Vision and Control - Fundamental Algorithms in MATLAB, Peter Corke, Springer, 2011 Author: Peter Corke Publisher: Springer ISBN: 978-3-642-20144-8
Kinematics • Kinematics is the branch of mechanics that studies the motion of a body or a system of bodies without considering its mass or the forces acting on it. • Forward (direct) Kinematics • Given: The values of the joint variables. • Required: The position and the orientation of the end effector. • Inverse Kinematics • Given : The position and the orientation of the end effector. • Required : The values of the joint variables.
Describing a Serial Manipulator • A serial manipulator comprises a set of bodies, called links, in a chain and connected by joints. • Each joint has one degree of freedom, either translational (prismatic joint) or rotational (a revolute joint). • Motion of the joint changes the relative angle or position of its neighboring links. • The joint structure of a robot can be described by a string such as • “RRRRRR” for the Puma • “RRPRRR” for the Stanford arm
Kinematics • For a manipulator with N joints numbered from 1 to N, there are N +1 links, numbered from 0 to N • Any given joint j connects links j-1 and j • Link 0 is the base of the manipulator and link N carries the end-effector
Why DH Notation • A systematic way of describing the geometry of a serial chain of links and joints was proposed by Denavit and Hartenberg in 1955 and is known today as Denavit-Hartenberg notation or simply D-H notation. • A very simple way of modeling robot links and joints that can be used for any kind of robot configuration. • This technique has became the standard way of representing robots and modeling their motions.
DH Techniques • A link j can be specified by two parameters, its length aj and its twist αj • Joints are also described by two parameters. The link offset dj is the distance from one link coordinate frame to the next along the axis of the joint. The joint angle θjis the rotation of one link with respect to the next about the joint axis.
DH Techniques • Link twistαi :the angle from the Zi-1 axis to the Ziaxis about the Xi axis. The positive sense for α is determined from zi-1 and ziby the right-hand rule. • Joint angle θithe angle between the Xi-1 and Xi axes about the Zi-1 axis.
DH Techniques • The four parameters for each link ai: link length αi: Link twist di: Link offset θi : joint angle • With the ith joint, a joint variable is qiassociated where
DH Techniques All joints are represented by the z-axis. • If the joint is revolute, the z-axis is in the direction of the axis of rotation as followed by the right hand rule. • If the joint is prismatic, the z-axis for the joint is along the direction of the liner movement.
DH Table - Example I The two link planar arm • Base frame O0 • All Z ‘s are normal to the page
