Mekanisme Robot - 3 SKS (Robot Mechanism) · • Three of them (x) cannot yield 3-dof robot because...

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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


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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Bit History

1994 : The Variax machine (Gidding & Lewis) shown at the Chicago exhibition on machine-tools


Applications of Parallel Manipulators

The Gough-Stewart platform for flight simulator

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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


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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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



10 architectures remains :

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3-PRR parallel manipulator



3-RRR parallel manipulator

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3-RPR parallel manipulator


3-RRR Parallel Manipulator

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3-RRR Parallel Manipulator

Inverse kinematics: 2 solutions for 𝜃𝑖

Direct kinematics: 8 solutions


3-RPR Parallel Manipulator

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3-RPR Parallel Manipulator

Example of Direct kinematics


Translational Parallel Manipulators

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Isotropic designs


3-UPU Parallel Manipulator

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Schönflies Parallel Manipulator


Passive legs

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3-PRS Parallel Manipulator

1. Find how many inverse kinematics solutions

2. Find how many direct kinematic solutions

Mekanisme Robot - 3 SKS (Robot Mechanism) · • Three of them (x) cannot yield 3-dof robot because...

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