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16/12/2016
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Mekanisme Robot - 3 SKS(Robot Mechanism)
Latifah Nurahmi, PhD
!! [email protected] !!
First Term - 2016/2017
C.250
Mekanisme Robot (Robot Mechanisms) by Latifah Nurahmi 2
Parallel Manipulator
• Moving platform
• Base
• m legs
• n joints in 1 leg
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Symmetrical Parallel Manipulator
• The number of legs equal to the number of dof
• The type and number of joints are arranged in identical pattern
• The number and location of actuated joints in all legs are the same
Mekanisme Robot (Robot Mechanisms) by Latifah Nurahmi 4
Bit History
1980 : The Delta robot patented by Remon Clavel (EPFL), probably the mostpopular (more than 400 robots sold in 20 years)
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Mekanisme Robot (Robot Mechanisms) by Latifah Nurahmi 5
Bit History
1994 : The Variax machine (Gidding & Lewis) shown at the Chicago exhibition on machine-tools
Mekanisme Robot (Robot Mechanisms) by Latifah Nurahmi 6
Applications of Parallel Manipulators
The Gough-Stewart platform for flight simulator
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Mekanisme Robot (Robot Mechanisms) by Latifah Nurahmi 7
Applications of Parallel Manipulators
Mekanisme Robot (Robot Mechanisms) by Latifah Nurahmi 8
Applications of Parallel Manipulators
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Applications of Parallel Manipulators
Mekanisme Robot (Robot Mechanisms) by Latifah Nurahmi 10
Actuators
Types of actuators in parallel manipulators:
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Symmetrical Parallel Manipulator
𝑚 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑒𝑔𝑠
𝐹 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑜𝑓
𝐿 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑜𝑜𝑝𝑠
𝐶 = 𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑎 𝑙𝑒𝑔
𝑓 = 𝑑𝑜𝑓 𝑜𝑓 𝑎 𝑗𝑜𝑖𝑛𝑡
𝑚 = 𝐹 = 𝐿 + 1
𝑘=1
𝑚
𝐶𝑘 =
𝑖=1
𝑗
𝑓𝑖
𝑗 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑗𝑜𝑖𝑛𝑡 𝑖𝑛 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑠𝑚
𝑘=1
𝑚
𝐶𝑘 = 𝜆 + 1 𝐹 −𝜆
Mekanisme Robot (Robot Mechanisms) by Latifah Nurahmi 12
Planar Parallel Manipulator
• Planar parallel manipulator 𝜆 = 3
• 3-dof 𝐹 = 3
• 3 legs 𝑚 = 3
• Substitute:
• Connectivity of 1 leg 𝐶𝑘 = 3
𝑘=1
𝑚
𝐶𝑘 = 𝜆 + 1 𝐹 −𝜆
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Planar Parallel Manipulator
𝐶𝑘 = 3, means:
• 1 leg should have 3-dof joints, If 1 leg consists of 2 l inks and 3
joints, each joint should be 1-dof.
• There are 21 3-dof legs in total.
• Three of them (x) cannot yield 3-dof robot because only 1-dof
would be controllable.
• There are eight pairs (~) that leads to kynematically equivalent
Mekanisme Robot (Robot Mechanisms) by Latifah Nurahmi 14
Planar Parallel Manipulator
10 architectures remains :
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Planar Parallel Manipulator
3-PRR parallel manipulator
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Planar Parallel Manipulator
3-RRR parallel manipulator
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Planar Parallel Manipulator
3-RPR parallel manipulator
Mekanisme Robot (Robot Mechanisms) by Latifah Nurahmi 18
3-RRR Parallel Manipulator
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3-RRR Parallel Manipulator
Inverse kinematics: 2 solutions for 𝜃𝑖
Direct kinematics: 8 solutions
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3-RPR Parallel Manipulator
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3-RPR Parallel Manipulator
Example of Direct kinematics
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Translational Parallel Manipulators
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Isotropic designs
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3-UPU Parallel Manipulator
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Schönflies Parallel Manipulator
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Passive legs
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3-PRS Parallel Manipulator
1. Find how many inverse kinematics solutions
2. Find how many direct kinematic solutions