mekanisme robot - 3 sks (robot mechanism) · 02/10/2016 3 mekanisme robot (robot mechanisms) by...

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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

Serial manipulators

n-dof serial manipulators:• Base link• n moving links• Open loop

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Definition of links and parameters

Link : 0 nJoint : 1 n

• Link 0 is the base• Link n is EE• Link 1 is connected to

the base by joint 1• Every link has 2 joints,

except base and EE• Link i has joint i at

proximal end• Link i has joint i+1 at

distal end

proximal distal


Denavit Hartenberg’s coordinate system

Coordinate system isattached by following rules(not for base & EE) :

• i : 0 n

• Frame i is attached to i link

proximal distal

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• zi – axis is aligned withthe axis of joint i+1

• xi – axis is commonperpendicular betweenzi-1 and zi

• xi – axis is directed fromjoint i to joint i+1

• y – axis is defined by the right-hand rule

proximal distal




• Two parallel axes:xi – axis is can be chosenarbitralily

• Two intersecting axes:cross product zi-1 x zi

proximal distal

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• 0 – coordinate is at the base

• z0 – axis is alligned withthe 1st joint

• n – coordinate isattached at EE

• xn – axis is normal to the last joint axis (n-1)

proximal distal



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Denavit Hartenberg’s parameters

• Hi-1 : intersection point between xi and zi-1

proximal distal• Oi-1 : origin of i-1th

coordinate system

• ai : distance between twoadjacent joint axes

• di : distance between twonormals of a joint axis



proximal distal

• θi : angle to rotatexi-1 – axis into xi – axis about zi-1 – axis

• αi : angle to rotatezi-1 – axis into zi – axis about xi – axis

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proximal distal

R-joint : • ai, αi, di constant • θi variable

P-joint : • ai, αi, θi constant • di variable


Denavit Hartenberg’s transformation matrix

Due to di along z-direction: 𝑇(𝑧, 𝑑) =

1 00 1

0 00 0

0 00 0

1 𝑑𝑖0 1

Due to θi about z-axis: 𝑇(𝑧, 𝜃) =

𝑐𝜃𝑖 −𝑠𝜃𝑖𝑠𝜃𝑖 𝑐𝜃𝑖

0 00 0

0 00 0

1 00 1

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Due to ai along x-direction: 𝑇(𝑥, 𝑎) =

1 00 1

0 𝑎𝑖0 0

0 00 0

1 00 1

Due to αi about x-axis: 𝑇(𝑥, 𝛼) =

1 00 𝑐𝛼𝑖

0 0−𝑠𝛼𝑖 0

0 𝑠𝛼𝑖0 0

𝑐𝛼𝑖 00 1



The transformation from EE to the base is:

𝑇𝑖𝑖−1 = 𝑇 𝑧, 𝑑𝑖 𝑇 𝑧, 𝜃𝑖 𝑇 𝑥, 𝑎𝑖 𝑇(𝑥, 𝛼𝑖)

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Denavit Hartenberg’s procedure

Define the DH-parameters!

Articulated robot 3-dof



1. Number the links and the joints, starting from the base to EE:• Link : 0 3• Joint : 1 3• The base is link 0 • EE is link 3Link 0

Link 1

Link 2

Link 3 Joint 1

Joint 2

Joint 3

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2. Define z0-axis, it is alignedwith the 1st joint axis

3. Define zi-axis, it is alignedwith joint i+1

4. Define xi-axis as commonnormal between i to i+1 joint axes

5. Because the joint axes are parallel, xi can be definedarbitrarily



2. Define z0-axis, it is alignedwith the 1st joint axis

3. Define zi-axis, it is alignedwith joint i+1

4. Define xi-axis as commonnormal between i to i+1 joint axes

5. Because the joint axes are parallel, xi can be definedarbitrarily

6. Define the parameters!

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Subtitute to the transformation matrix:

Mutliply the transformation matrices:

𝐴30 = 𝐴1

0 𝐴21 𝐴3

2

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Assignment 1

Find the DH-parameters of SCARA Robot !


Assignment 1

Let’s see the structures !

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Assignment 1

Link 0

Link 1Link 2

Link 3

Link 4


Assignment 1

Link 0

Link 1Link 2

Link 3

Link 4

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Assignment 2

Find the DH-parameters of Scorbot !


Assignment 2

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Assignment 2

mekanisme robot - 3 sks (robot mechanism) · 02/10/2016 3 mekanisme robot (robot mechanisms) by...

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