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20MTT62 – MECHANICS OF SERIAL MANIPULATOR

COURSE OUTCOMES

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On completion of the course the students will be able to

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CO1:

interpret the features of a serial manipulator with end effector (K3)

CO2:

compute position and orientation based on robot kinematic structure (K3)

CO3:

develop the forward and inverse kinematics for serial manipulator (K3)

CO4:

analyse the differential motions and velocity of serial manipulator (K3)

CO5:

formulate trajectory and robot dynamics (K3)

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UNIT – I

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9

Fundamentals of Serial Manipulator: History of robotics - Components of industrial robot – Joint notation scheme - Classification of robots - Robot specifications - Precision of movements - End Effectors: Types of end effectors -Mechanical Gripper: Gripper force analysis - Vacuum cup - Magnetic gripper - Special types of grippers -. Programming modes - Robot applications.

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UNIT – II

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9

Frame Transformation: Descriptions: Position, Orientation and Frames - Matrix representation: Point, vector, frame and rigid body - Homogeneous Transformation matrices – Representation: Translation, Rotational and Combined transformation – Simple problems.

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UNIT – III

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9

Robot Kinematics: Forward and inverse kinematics – Equations for position and orientation – Denavit-Hartenberg representation of forward kinematic equations: Two and Three link planer, PUMA and SCARA - Inverse kinematic equation: Two and three link planar.

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UNIT – IV

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9

Differential Motions and Velocities: Introduction - Linear and angular velocities of a rigid body - Velocity propagation – Derivation of Jacobian for serial manipulator – Identification of singularities.

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UNIT – V

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9

Trajectory Planning and Robot Dynamics: Joint space trajectory - Cartesian space trajectory – Simple problems. Robot Dynamics: Acceleration of a rigid body - Inertia of a link - Equation of motion: Legrangian formulation – Newton Euler formulation.

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TOTAL: 45

BOOKS:

1.

Saeed B. Niku, "Introduction To Robotics: Analysis, Control, Applications", 2nd Edition, Wiley India Pvt. Ltd., Noida, 2011.

2.

Groover M.P., "Industrial Robotics, Technology, Programming and Applications", 2nd Edition, McGraw-Hill, New Delhi, 2017.

3.

Craig John J., "Introduction to Robotics: Mechanics and Control", 3rd Edition, Pearson Education, New Delhi, 2017.

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Conventions for Describing Vectors, Frames & Transformations

( - Transformation of robot relative to the Universe, where Universe is a fixed frame)

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Representation of a Point in Space

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Representation of a Vector in Space

Vector starts at point A and ends at point B: PAB = (Bx – Ax) i + (By – Ay) j + (Bz – Az) k

Vector starts at origin:

P= axi + byj + czk

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Representation of a Vector in Space

Vector starts at origin: P= axi + byj + czk

Vector in matrix form :

By including a scale factor w:

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Representation of a Vector in Space

Scaling Factor : W

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  • Any number and, as it changes, it can change the overall size of the vector (similar to the zooming function in computer graphics)
  • w > 1 --- All vector components enlarge
  • w < 1 --- All vector components become smaller
  • w = 1 --- Size of these components remains unchanged
  • w = 0 --- ax, by, and cz will be infinity --- Representation of Direction vector

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Px = ax X w = 3 X 2 = 6

Py = by X w = 5 X 2 = 10

Pz = cz X w = 2 X 2 = 4

A vector is described as P = 3i + 5j + 2k. Express the vector in matrix form: (a) With a scale factor of 2. (b) If it were to describe a direction as a unit vector.

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A vector p is 5 units long and is in the direction of a unit vector q described below. Express the vector in matrix form.

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n - normal

o - orientation

a - approach

a-axis :

Approach-axis

o-axis :

Orientation-axis

n-axis :

Normal axis

x, y, z -- Fixed Universe reference frame (Fxyz)

n, o, a - Moving frame (Fnoa) relative to the reference frame

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Representation of a Frame at the Origin of a Fixed Reference Frame

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Representation of a Frame Relative to a Fixed Reference Frame

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Representation of a Rigid Body

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Homogeneous Transformation Matrices

Orientation

Position

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Representation of a Pure Translational

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Representation of a Pure Rotation about an Axis

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Rotational Matrix

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Representation of Combined Transformations

Three successive transformations relative to the reference frame Fxyz:

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  1. Rotation of α degrees about the x-axis

2. Followed by a translation of (l1,l2,l3) (relative to the x, y and z axes respectively)

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3. Followed by a rotation of β degrees about the y-axis.

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