Page 1 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, N=no of links=1 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 Where l= no. of links 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, N=no of links=1 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 Where l= no. of links 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 menu of the pageRead More

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