The document discusses fundamental concepts of manipulators and robotics including: - Manipulators are constructed of connected links and joints that allow movement. Actuators like motors cause the links to move and end effectors can grasp objects. - Position and orientation of objects are described using coordinate frames. Forward and inverse kinematics are used to relate joint angles to end effector position and vice versa. - The Jacobian relates joint velocities to end effector velocity. Trajectory generation determines joint motion functions to smoothly move between positions. - A robot's configuration space specifies all points of the robot. Degrees of freedom refer to the minimum coordinates needed to define the configuration. - Common robot joints include revolute, prismatic,

1. CHAPTER -2
MANIPULATORS
BASIC CONCEPTS
AHMED KHALID AHMED
COMPUTER AND CONTROL ENGINEERING + MECH.
MECHATRONICS ENGINEERING
FOURTH STAGE

2. Background
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:The Adept 6 manipulator has six rotational joints and is popular in many
applications. Courtesy of Adept Tecimology, Inc

3. Background
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LINKS

4. Background
Links and Joints
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5. Background
Links and Joints
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6. Background
A Robot is mechanically constructed by connecting a set of bodies,
called links, to each other using various types of joints.
Actuators such as electric motors deliver forces or torque that
cause the robots link to move.
An end effector such as gripper or hand for grasping and
manipulating objects , is attached to a specific link.
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7. Background
1. Our focuses on the mechanics and control of the most important form of the industrial
robot, the mechanical manipulator and Wheeled mobile robots.
2. The Manipulator type robots will be covered first.
3. The distinction lies somewhere in the sophistication of the programmability of the device—
if a mechanical device can be programmed to perform a wide variety of applications, it is
probably an industrial robot.
4. Machines which are for the most part limited to one class of task are considered fixed
automation.
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8. THE MECHANICS AND CONTROL OF MECHANICAL
MANIPULATORS
Description of position and orientation
In the study of robotics, we are constantly concerned with the location of objects in
three-dimensional space.
These objects are the links of the manipulator, the parts and tools with which it deals, and other
objects in the manipulator's environment.
At a crude but important level, these objects are described by just two attributes: position and
orientation.
Naturally, one topic of immediate interest is the manner in which we represent these quantities
and manipulate them mathematically.
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9. In order to describe the position and orientation of a body in space, we will always attach a coordinate
system, or frame, rigidly to the object.
We then proceed to describe the position and orientation of this frame with respect to some
reference coordinate system.
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THE MECHANICS AND CONTROL OF
MECHANICAL MANIPULATORS

10. THE MECHANICS AND CONTROL OF
MECHANICAL MANIPULATORS
Coordinate systems or "frames" are
attached to the manipulator and to
objects in the environment.
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Any frame can serve as a reference system
within which to express the position and
orientation of a body, so we often think of
transforming or changing the description
of these attributes of a body from one
frame to another.

11. Forward kinematics of manipulators
Kinematics is the science of motion that treats motion without regard to the forces
which cause it.
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12. Forward kinematics of manipulators
The study of the kinematics of manipulators refers to all the geometrical and time-based
properties of the motion.
Manipulators consist of nearly rigid links, which are connected by joints that allow relative
motion of neighboring links .
These joints are usually instrumented with position sensors, which allow the relative position of
neighboring links to be measured.
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13. Forward kinematics of manipulators
Forward kinematics. is the static geometrical problem of computing the position and orientation of
the end-effector of the manipulator.
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Kinematic equations describe the
tool frame relative to the base frame
as a function of the joint variables.

14. Forward kinematics of manipulators
If you given a set of joint angles, the forward kinematic
problem is to compute the position and orientation of the
tool frame relative to the base frame. Sometimes, we think
of this as changing the representation of manipulator
position from a joint space description into a Cartesian
space description.
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15. Inverse kinematics of manipulators
Inverse kinematics. This problem is posed as follows: Given the
position and orientation of the end-effector of the manipulator,
calculate all possible sets of joint angles that could be used to attain
this given position and orientation.
In the case of an artificial system like a robot, we will need to create
an algorithm in the control computer that can make this calculation.
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16. Inverse kinematics of manipulators
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For a given position and orientation
of the tool frame, values for the
joint variables can be calculated via
the inverse kinematics.

17. Velocities, static forces, singularities
In addition to dealing with static positioning problems, we may wish to analyze manipulators in
motion.
Often, in performing velocity analysis of a mechanism, it is convenient to define a matrix quantity
called the Jacobian of the manipulator.
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18. Velocities, static forces, singularities
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The geometrical relationship between joint rates and velocity of the
end-effector can be described in a matrix called the Jacobian.

19. Trajectory generation
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A common way of causing a manipulator to move from here to there in a smooth,
controlled fashion is to cause each joint to move as specified by a smooth function
of time.

20. Trajectory generation
Commonly, each joint starts and ends its motion at
the same time, so that the appears coordinated.
Exactly how to compute these motion functions is
the problem of trajectory generation.
Often, a path is described not only by a desired
destination but also by some intermediate
locations, or via points, through which the
manipulator must pass en route to the destination.
In such instances the term spline is sometimes used
to refer to a smooth function that passes through a
set of via points.
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21. Configuration Space
The most fundamental question you can ask about a robot is, "Where is it?"
The answer to this question is the robot's configuration, which is a specification of the positions
of all the points of the robot.
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22. Configuration Space
Example:
A door is represented by a single number (Ɵ) about its hinge.
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23. Position and Orientation
Ex. a point (planar surface) The configuration of a point on a plane can be described by two
coordinates, (x,y)
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24. Position and Orientation
Ex. Coin (planar surface) The configuration of a coin lying heads up on a flat table can be
described by three coordinates: two coordinates (x,y) that specify the location of a particular
point on the coin, and one coordinate(θ) that specifies the coin’s orientation.
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25. Degrees of freedom (DoF)
The number of degrees of freedom (DOF) of a robot is the smallest number of real-valued
coordinates needed to represent its configuration.
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DOF= DOF= DOF=

26. Degrees of freedom (DoF)
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27. Degrees of freedom (DoF)
Generally, For planner
we have 3 DOF and for
Spacial the DOF is 6.
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28. Robot Joints
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29. Robot Joints
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30. Robot Joints
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31. Robot Joints
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32. Serial , Parallel and Hybrid Mechanisms
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33. Serial , Parallel and Hybrid Mechanisms
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34. DoF ; Grubler’s Formula
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35. EXAMPLE
(Four-bar linkage and slider–crank mechanism). The planar four bar linkage shown in Figure
consists of four links (one of them ground). arranged in a single closed loop and connected by
four revolute joints. Since all the links are confined to move in the same plane, we have m = 3.
Substituting N = 4, J = 4, and fi = 1, i = 1, . . . , 4, into Grubler’s formula, we see that the four-bar
linkage has one degree of freedom.
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36. EXAMPLE
The slider–crank closed-chain mechanism can be analyzed in two ways:
(i) the mechanism consists of three revolute joints and one prismatic joint (J = 4 and each fi = 1)
and four links (N = 4, including the ground link), or
(ii) the mechanism consists of two revolute joints (fi = 1) and one RP joint (the RP joint is a
concatenation of a revolute and prismatic joint, so that fi = 2) and three links (N = 3; remember
that each joint connects precisely two bodies). In both cases the mechanism has one degree of
freedom.
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37. Find the DOF?
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38. Assignment 2
Find the actual degree of freedom using Grublers Formula and then indicate if the formula can
be applied for such kind of mechanisms or not?
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39. Workspace
The workspace of robot manipulator is defined as the set of points that can be reached by its
end-effector
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40. Workspace
Example: Sketch the fingertip workspace of the three-link manipulator for the case l1= 15.0, l2 =
10.0, and l3 = 3.0.
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41. End of Chapter-1
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