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**Introduction to ROBOTICS**

Kinematics of Robot Manipulator PROF.UJWAL HARODE UJWALHARODE

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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 UJWALHARODE

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**Review What is a robot? Why use robots?**

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? Perform 4A tasks in 4D environments 4A: Automation, Augmentation, Assistance, Autonomous 4D: Dangerous, Dirty, Dull, Difficult UJWALHARODE

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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 UJWALHARODE

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**(Selective Compliance Assembly Robot Arm)**

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

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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 UJWALHARODE

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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 UJWALHARODE

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**What is Kinematics Forward kinematics Given joint variables**

End-effector position and orientation, -Formula? UJWALHARODE

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**Joint variables -Formula?**

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

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Example 1 UJWALHARODE

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**Robot Reference Frames World frame Joint frame Tool frame**

Preliminary Robot Reference Frames World frame Joint frame Tool frame T T W R UJWALHARODE

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**Coordinate Transformation**

Reference coordinate frame –XYZ Body-attached frame-ijk Point represented in XYZ Point represented in uvw: Two frames coincide UJWALHARODE

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**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 Properties of orthonormal co-ordinate frame.unitvectors are mutually perpendicular UJWALHARODE

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**Coordinate Transformation**

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

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

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**Rotation about x-axis with**

Basic Rotation Matrix Rotation about x-axis with UJWALHARODE

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**Rotation about y-axis with :**

Rotation about z-axis with : UJWALHARODE

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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. UJWALHARODE

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**A sequence of finite rotations**

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 UJWALHARODE

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**Find the rotation matrix for the following operations:**

Pre-multiply if rotate about the OXYZ axes Post-multiply if rotate about the OUVW axes UJWALHARODE

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**Homogeneous Transformation**

Special cases 1. Translation 2. Rotation Homogeneous transformation matrix Homogeneous transformation matrix UJWALHARODE

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**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 UJWALHARODE

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**Description of Roll Pitch Yaw**

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

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