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# Manipulators Mechanisms-I, Robots mechanisms Mechanical Engineering Notes | EduRev

## Mechanical Engineering : Manipulators Mechanisms-I, Robots mechanisms Mechanical Engineering Notes | EduRev

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Module 2 : Robots mechanisms
Lecture 5 : Manipulators Mechanisms-I
Objectives
In this lecture we will learn about
Degrees of freedom
Parallel Manipulators
“Teaching” the manipulator

Degrees Of Freedom

It is required to find DOF for a manipulator which in turn decides the number of actuators required. The
task is relatively straightforward for open chains –serial manipulators. In most of these, the chain is
composed of links connected through revolute or prismatic pairs. The degrees of freedom simply turn out to
be the number of moving links in the open chain - and the number of actuators will equal the degrees of
freedom. The word “axis” is often used instead of degrees of freedom. Thus a manipulator with six moving
links and as many revolute pairs is called a 6-axis manipulator. Note that the actuator used to power the
gripper (open and close fingers etc) is not counted as an “axis” – since the function of the actuator on the
gripper is solely to open and close the fingers. Also, the actuator for the gripper does not contribute to the
positioning and orienting capability of the end-effector.
Closed chains.

Figure 5.1.1
To find the DOF of mechanism in robot, Gubler's formula for closed chains or given set of n links is applied.
1.
For the 5R mechanism shown above Figure 5.1.1, let
Jr- no of revolute joints; Jp – no of prismatic joints
Then Gublers formula states that DOF=3(n-1)-2Jr-2Jp
For above mechanism of 5R; DOF=3(5-1)-2x5=2
2. For 4RP mechanism, n=5, Jr=4, Jp=1 therefore DOF= 3(5-1)-2x4-2x1=2
Page 2

Module 2 : Robots mechanisms
Lecture 5 : Manipulators Mechanisms-I
Objectives
In this lecture we will learn about
Degrees of freedom
Parallel Manipulators
“Teaching” the manipulator

Degrees Of Freedom

It is required to find DOF for a manipulator which in turn decides the number of actuators required. The
task is relatively straightforward for open chains –serial manipulators. In most of these, the chain is
composed of links connected through revolute or prismatic pairs. The degrees of freedom simply turn out to
be the number of moving links in the open chain - and the number of actuators will equal the degrees of
freedom. The word “axis” is often used instead of degrees of freedom. Thus a manipulator with six moving
links and as many revolute pairs is called a 6-axis manipulator. Note that the actuator used to power the
gripper (open and close fingers etc) is not counted as an “axis” – since the function of the actuator on the
gripper is solely to open and close the fingers. Also, the actuator for the gripper does not contribute to the
positioning and orienting capability of the end-effector.
Closed chains.

Figure 5.1.1
To find the DOF of mechanism in robot, Gubler's formula for closed chains or given set of n links is applied.
1.
For the 5R mechanism shown above Figure 5.1.1, let
Jr- no of revolute joints; Jp – no of prismatic joints
Then Gublers formula states that DOF=3(n-1)-2Jr-2Jp
For above mechanism of 5R; DOF=3(5-1)-2x5=2
2. For 4RP mechanism, n=5, Jr=4, Jp=1 therefore DOF= 3(5-1)-2x4-2x1=2

Figure 5.1.2
3.
Figure 5.1.2 for 6R bar planer mechanism n=6, Jr= 6, Jp=0
Therefore Mechanism DOF = 3(6-1)-2x6=15-12=3
Work space of closed chains will be less than that of open chains.

Parallel Chains

Figure5.2.1
1)
Stewart platform: Here 2 rings top & bottom are connected
together through prismatic links and having ball & socket joint
at bottom and hooks joint at top. Figure 5.2.1 beside. Stewart
platform finds application in aircraft simulator where pilots are
trained

Applying Grublers criterion for closed chains,
Js=no of spherical joints=6
Jh= no of hook's joint=6
Jr= no of revolute joint=0
Jp= no of prismatic joints=6
DOF = F=6(l-n-1) + S fi
N= no of joints
fi = DOF with ith joint
Therefore, F = 6(14-18-1) + 36 = 6
Teaching and Measurement

Manipulators may be used as measuring tools as
shown in figure 5.3.1. With link lengths and joint
angles known we can determine position &
Page 3

Module 2 : Robots mechanisms
Lecture 5 : Manipulators Mechanisms-I
Objectives
In this lecture we will learn about
Degrees of freedom
Parallel Manipulators
“Teaching” the manipulator

Degrees Of Freedom

It is required to find DOF for a manipulator which in turn decides the number of actuators required. The
task is relatively straightforward for open chains –serial manipulators. In most of these, the chain is
composed of links connected through revolute or prismatic pairs. The degrees of freedom simply turn out to
be the number of moving links in the open chain - and the number of actuators will equal the degrees of
freedom. The word “axis” is often used instead of degrees of freedom. Thus a manipulator with six moving
links and as many revolute pairs is called a 6-axis manipulator. Note that the actuator used to power the
gripper (open and close fingers etc) is not counted as an “axis” – since the function of the actuator on the
gripper is solely to open and close the fingers. Also, the actuator for the gripper does not contribute to the
positioning and orienting capability of the end-effector.
Closed chains.

Figure 5.1.1
To find the DOF of mechanism in robot, Gubler's formula for closed chains or given set of n links is applied.
1.
For the 5R mechanism shown above Figure 5.1.1, let
Jr- no of revolute joints; Jp – no of prismatic joints
Then Gublers formula states that DOF=3(n-1)-2Jr-2Jp
For above mechanism of 5R; DOF=3(5-1)-2x5=2
2. For 4RP mechanism, n=5, Jr=4, Jp=1 therefore DOF= 3(5-1)-2x4-2x1=2

Figure 5.1.2
3.
Figure 5.1.2 for 6R bar planer mechanism n=6, Jr= 6, Jp=0
Therefore Mechanism DOF = 3(6-1)-2x6=15-12=3
Work space of closed chains will be less than that of open chains.

Parallel Chains

Figure5.2.1
1)
Stewart platform: Here 2 rings top & bottom are connected
together through prismatic links and having ball & socket joint
at bottom and hooks joint at top. Figure 5.2.1 beside. Stewart
platform finds application in aircraft simulator where pilots are
trained

Applying Grublers criterion for closed chains,
Js=no of spherical joints=6
Jh= no of hook's joint=6
Jr= no of revolute joint=0
Jp= no of prismatic joints=6
DOF = F=6(l-n-1) + S fi
N= no of joints
fi = DOF with ith joint
Therefore, F = 6(14-18-1) + 36 = 6
Teaching and Measurement

Manipulators may be used as measuring tools as
shown in figure 5.3.1. With link lengths and joint
angles known we can determine position &

Figure 5.3.1
orientation of end effector. This technique is used
for “teaching”.
Recap
In this course you have learnt the following
Gublers criterion for mechanism analysis
Spatial robot of Stewart Platform and its DOF
Application of robots for inspection purposes

Congratulations, you have finished Lecture 5. To view the next lecture select it from the left hand side

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