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Introduction to ROBOTICS Kinematics of Robot Manipulator PROF.UJWAL HARODE UJWALHARODE1

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Outline Review Robot Manipulators -Robot Configuration -Robot Specification Number of Axes, DOF Precision, Repeatability Kinematics -Preliminary World frame, joint frame, end-effector frame Rotation Matrix, composite rotation matrix Homogeneous Matrix -Direct kinematics Denavit-Hartenberg Representation Examples -Inverse kinematics UJWALHARODE2

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Review What is a robot? By general agreement a robot is: A programmable machine that imitates the actions or appearance of an intelligent creature–usually a human. To qualify as a robot, a machine must be able to: 1) Sensing and perception: get information from its surroundings 2) Carry out different tasks: Locomotion or manipulation, do something physical–such as move or manipulate objects 3) Re-programmable: can do different things 4) Function autonomously and/or interact with human beings Why use robots? UJWALHARODE3 –Perform 4A tasks in 4D environments 4A: Automation, Augmentation, Assistance, Autonomous 4D: Dangerous, Dirty, Dull, Difficult

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Manipulators Robot arms, industrial robot Rigid bodies (links) connected by joints Joints: revolute or prismatic Drive: electric or hydraulic End-effector (tool) mounted on a flange or plate secured to the wrist joint of robot UJWALHARODE4

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Manipulators Robot Configuration SCARA: RRP (Selective Compliance Assembly Robot Arm) 5 Cartesian: PPP Cylindrical: RPP Spherical: RRP Articulated: RRR Hand coordinate: n: normal vector; s: sliding vector; a: approach vector, normal to the tool mounting plate

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Manipulators Motion Control Methods Point to point control a sequence of discrete points spot welding, pick-and-place, loading & unloading Continuous path control follow a prescribed path, controlled- path motion Spray painting, Arc welding, Gluing UJWALHARODE6

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Manipulators Robot Specifications Number of Axes Major axes, (1-3) => Position the wrist Minor axes, (4-6) => Orient the tool Redundant, (7-n) => reaching around obstacles, avoiding undesirable configuration Degree of Freedom (DOF) Workspace Payload (load capacity) Precision v.s. Repeatability UJWALHARODE7

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What is Kinematics Forward kinematics Given joint variables End-effector position and orientation, - Formula? UJWALHARODE8

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9 What is Kinematics Inverse kinematics End effector position and orientation Joint variables -Formula?

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UJWALHARODE10 Example 1

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UJWALHARODE11 Preliminary Robot Reference Frames 1.World frame 2.Joint frame 3.Tool frame W T T R

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UJWALHARODE12 Coordinate Transformation O, O’ Reference coordinate frame –XYZ Body-attached frame-ijk Point represented in XYZ Point represented in uvw: Two frames coincide

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UJWALHARODE13 Properties: Dot Product Let and be arbitrary vectors in and be the angle from to, then Properties of orthonormal co-ordinate frame Unit vectors are mutually perpendicular

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UJWALHARODE14 Coordinate Transformation Reference coordinate frame OXYZ Body-attached frame O’uvw O, O’ How to relate the coordinate in these two frames?

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UJWALHARODE15 Basic Rotation –,, and represent the projections of onto OX, OY, OZ axes, respectively – Since

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Basic Rotation Matrix Rotation about x-axis with UJWALHARODE16

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UJWALHARODE17 Rotation about y-axis with : Rotation about z-axis with :

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UJWALHARODE18 Example 2 A point is attached to a rotating frame, the frame rotates 60 degree about the OZ axis of the reference frame. Find the coordinates of the point relative to the reference frame after the rotation.

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UJWALHARODE19 Composite Rotation Matrix A sequence of finite rotations – matrix multiplications do not commute – rules: if rotating coordinate O-U-V-W is rotating about principal axis of OXYZ frame, then Pre-multiply the previous (resultant) rotation matrix with an appropriate basic rotation matrix if rotating coordinate OUVW is rotating about its own principal axes, then post-multiply the previous (resultant) rotation matrix with an appropriate basic rotation matrix

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UJWALHARODE20 Find the rotation matrix for the following operations: Pre-multiply if rotate about the OXYZ axes Post-multiply if rotate about the OUVW axes

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UJWALHARODE21 Homogeneous Transformation Special cases 1. Translation 2. Rotation Homogeneous transformation matrix

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UJWALHARODE22 Homogeneous Transformation Composite Homogeneous Transformation Matrix Rules: – Transformation (rotation/translation) w.r.t (X,Y,Z) (OLD FRAME), using pre-multiplication – Transformation (rotation/translation) w.r.t (U,V,W) (NEW FRAME), using post-multiplication

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UJWALHARODE23 Orientation Representation Description of Roll Pitch Yaw X Y Z YAW PITCH ROLL

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