The document describes the parameters and forward kinematics of a 5 degree-of-freedom robotic arm. It defines each link of the arm as a revolute joint and specifies the link lengths, offsets, and joint variables. It then calculates and plots the forward kinematics of the arm as the first joint variable is varied from 0 to pi/2.

1. 1
%%Abdelmajid belkhaoui
%on utilise Peter CorkeDH_Parameter
L1=10.25; L2=9; L3=9; L5=6.25
%L(i)= Link ([Theta d a alpha])
L(1)= Link ([0 L1 0 pi/2])
L(1).jointtype='R'
L(2)= Link ([0 0 L2 0])
L(2).jointtype='R'
L(3)= Link ([0 0 L3 0])
L(3).jointtype='R'
L(4)= Link ([0 0 0 pi/2])
L(4).jointtype='R'
L(5)= Link ([0 L5 0 0])
L(5).jointtype='R'
Rob=SerialLink(L)Rob.fkine([
0 pi/4 pi/4 0 0])syms t1 t2
t3 t4 t5Rob.fkine([t1 t2 t3
t4 t5])
simplify(Rob.fkine([t1 t2 t3 t4
t5]))Rob.name='RhinoXR1'
Rob.plot([0 0 0 0
0])fort1=0:0.1:pi/2
Rob.plot([t1 0 0 0
0])pause(0.25)
end
L5=6.2500
L =
Revolute(std): theta=q1 d=10.25 a=0 alpha=1.571
offset=0
Revolute(std): theta=q2 d=0 a=9 alpha=0
offset=0
Revolute(std): theta=q3 d=0 a=9 alpha=0
offset=0
Revolute(std): theta=q4 d=0 a=0 alpha=1.571
offset=0
Revolute(std): theta=q5 d=6.25 a=0 alpha=0
offset=0
L =
Revolute(std): theta=q1 d=10.25 a=0 alpha=1.571
offset=0
Revolute(std): theta=q2 d=0 a=9 alpha=0
offset=0
Revolute(std): theta=q3 d=0 a=9 alpha=0
offset=0
Revolute(std): theta=q4 d=0 a=0 alpha=1.571
offset=0
Revolute(std): theta=q5 d=6.25 a=0 alpha=0
offset=0

2. 2
L =
Revolute(std): theta=q1 d=10.25 a=0 alpha=1.571
offset=0
Revolute(std): theta=q2 d=0 a=9 alpha=0
offset=0
Revolute(std): theta=q3 d=0 a=9 alpha=0
offset=0
Revolute(std): theta=q4 d=0 a=0 alpha=1.571
offset=0
Revolute(std): theta=q5 d=6.25 a=0 alpha=0
offset=0
L =
Revolute(std): theta=q1 d=10.25 a=0 alpha=1.571
offset=0
Revolute(std): theta=q2 d=0 a=9 alpha=0
offset=0
Revolute(std): theta=q3 d=0 a=9 alpha=0
offset=0
Revolute(std): theta=q4 d=0 a=0 alpha=1.571
offset=0
Revolute(std): theta=q5 d=6.25 a=0 alpha=0
offset=0
L =
Revolute(std): theta=q1 d=10.25 a=0 alpha=1.571
offset=0
Revolute(std): theta=q2 d=0 a=9 alpha=0
offset=0
Revolute(std): theta=q3 d=0 a=9 alpha=0
offset=0
Revolute(std): theta=q4 d=0 a=0 alpha=1.571
offset=0
Revolute(std): theta=q5 d=6.25 a=0 alpha=0
offset=0
Rob =
noname:: 5 axis, RRRRR, stdDH, slowRNE
+---+-----------+-----------+-----------+-----------+-----------+
| j | theta | d | a | alpha | offset |
+---+-----------+-----------+-----------+-----------+-----------+
| 1| q1| 10.25| 0| 1.5708| 0|
| 2| q2| 0| 9| 0| 0|
| 3| q3| 0| 9| 0| 0|
| 4| q4| 0| 0| 1.5708| 0|
| 5| q5| 6.25| 0| 0| 0|
+---+-----------+-----------+-----------+-----------+-----------+
ans =
0 0 1 12.61

3. 3
0 -1 0 0
1 0 0 25.61
0 0 0 1
[ cos(t5)*((81129638414606686663546605165575*cos(t1
+ t2 + t3 + t4))/162259276829213363391578010288128
+ (81129638414606676728031405122553*cos(t2 - t1
+ t3 + t4))/162259276829213363391578010288128) -
sin(t5)*((403032377821159448978357750059338280708391237583*sin(t2-
t1 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
+ (403032377821159498335588895202304015643716683825*sin(t1 + t2 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
- sin(t1)), -
cos(t5)*((403032377821159448978357750059338280708391237583*sin(t2-
t1 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
+ (403032377821159498335588895202304015643716683825*sin(t1 + t2 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
- sin(t1)) - sin(t5)*((81129638414606686663546605165575*cos(t1
+ t2 + t3 + t4))/162259276829213363391578010288128
+ (81129638414606676728031405122553*cos(t2 - t1
+ t3 +
t4))/162259276829213363391578010288128),(811296
38414606676728031405122553*sin(t2 - t1
+ t3 + t4))/162259276829213363391578010288128
+ (81129638414606686663546605165575*sin(t1 + t2
+ t3 + t4))/162259276829213363391578010288128
+(4967757600021511*sin(t1))/81129638414606681695789005144064
,(2028240960365166918200785128063825*sin(t2 - t1
+ t3 + t4))/649037107316853453566312041152512
+ (730166745731460090552282646102977*cos(t1
- t2))/162259276829213363391578010288128
+(730166745731460179971919446490175*cos(t1
+t2+t3))/162259276829213363391578010288128
+(730166745731460090552282646102977*cos(t2-t1 +
t3))/162259276829213363391578010288128
+(2028240960365167166588665129139375*sin(t1+t2
+ t3 + t4))/649037107316853453566312041152512
+ (730166745731460179971919446490175*cos(t1
+ t2))/162259276829213363391578010288128
+(124193940000537775*sin(t1))/324518553658426726783156020576256
]
[ - sin(t5)*(cos(t1) -
(403032377821159498335588895202304015643716683825*cos(t1 + t2 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
+ (403032377821159448978357750059338280708391237583*cos(t2 - t1 + t3
+t4))/13164036458569648337239753460458804039861886925068638906788872192
)
-(cos(t5)*(81129638414606676728031405122553*sin(t2-
t1+t3+t4)-81129638414606686663546605165575*sin(t1

4. 4
+ t2 + t3 +
t4)))/162259276829213363391578010288128,sin(t5)*((
81129638414606676728031405122553*sin(t2
- t1 + t3 + t4))/162259276829213363391578010288128 -

5. 5
(81129638414606686663546605165575*sin(t1 + t2 + t3
+t4))/162259276829213363391578010288128) - cos(t5)*(cos(t1) -
(403032377821159498335588895202304015643716683825*cos(t1 + t2 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
+ (403032377821159448978357750059338280708391237583*cos(t2 - t1 + t3
+t4))/13164036458569648337239753460458804039861886925068638906788872192)
,(81129638414606676728031405122553*cos(t2 - t1
+ t3 + t4))/162259276829213363391578010288128 -
(4967757600021511*cos(t1))/81129638414606681695789005144064
- (81129638414606686663546605165575*cos(t1 + t2
+ t3 +
t4))/162259276829213363391578010288128,(730166
745731460090552282646102977*sin(t1
- t2))/162259276829213363391578010288128
+(730166745731460179971919446490175*sin(t1
+t2+t3))/162259276829213363391578010288128
-(730166745731460090552282646102977*sin(t2-t1 +
t3))/162259276829213363391578010288128 -
(2028240960365167166588665129139375*cos(t1+t2
+ t3 + t4))/649037107316853453566312041152512
+ (730166745731460179971919446490175*sin(t1
+ t2))/162259276829213363391578010288128 -
(124193940000537775*cos(t1))/324518553658426726783156020576256
+ (2028240960365166918200785128063825*cos(t2 - t1 + t3
+t4))/649037107316853453566312041152512]
[
sin(t2 + t3 + t4)*cos(t5) + sin(t5)*((4967757600021511*cos(t2
+ t3 + t4))/81129638414606681695789005144064
+4967757600021511/81129638414606681695789005144064)
,
cos(t5)*((4967757600021511*cos(t2
+ t3 + t4))/81129638414606681695789005144064
+4967757600021511/81129638414606681695789005144064)-
sin(t2 + t3 + t4)*sin(t5),
24678615572571482867467662723121/658201822928482416861987673022940201993094346253
- cos(t2 + t3 + t4),
9*sin(t2 + t3) - (25*cos(t2 + t3 + t4))/4 + 9*sin(t2)
+269862747400677790913414945939406099782557996250978784280739957961/2632807291713

6. 6
9

7. 7
[
0,
0,
0,
1]
[ cos(t5)*((81129638414606686663546605165575*cos(t1
+ t2 + t3 + t4))/162259276829213363391578010288128
+ (81129638414606676728031405122553*cos(t2 - t1
+ t3 + t4))/162259276829213363391578010288128) -
sin(t5)*((403032377821159448978357750059338280708391237583*sin(t2-
t1 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
+ (403032377821159498335588895202304015643716683825*sin(t1 + t2 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
- sin(t1)), -
cos(t5)*((403032377821159448978357750059338280708391237583*sin(t2-
t1 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
+ (403032377821159498335588895202304015643716683825*sin(t1 + t2 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
- sin(t1)) - sin(t5)*((81129638414606686663546605165575*cos(t1
+ t2 + t3 + t4))/162259276829213363391578010288128
+ (81129638414606676728031405122553*cos(t2 - t1
+ t3 +
t4))/162259276829213363391578010288128),(811296
38414606676728031405122553*sin(t2 - t1
+ t3 + t4))/162259276829213363391578010288128
+ (81129638414606686663546605165575*sin(t1 + t2

8. 8
+ t3 + t4))/162259276829213363391578010288128 +

9. 9
(4967757600021511*sin(t1))/81129638414606681695789005144064,
(2028240960365166918200785128063825*sin(t2 - t1
+ t3 + t4))/649037107316853453566312041152512
+ (730166745731460090552282646102977*cos(t1
- t2))/162259276829213363391578010288128
+(730166745731460179971919446490175*cos(t1
+t2+t3))/162259276829213363391578010288128
+(730166745731460090552282646102977*cos(t2-t1 +
t3))/162259276829213363391578010288128
+(2028240960365167166588665129139375*sin(t1+t2
+ t3 + t4))/649037107316853453566312041152512
+ (730166745731460179971919446490175*cos(t1
+ t2))/162259276829213363391578010288128
+(124193940000537775*sin(t1))/324518553658426726783156020576256
]
[ - sin(t5)*(cos(t1) -
(403032377821159498335588895202304015643716683825*cos(t1 + t2 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
+ (403032377821159448978357750059338280708391237583*cos(t2 - t1 + t3
+t4))/13164036458569648337239753460458804039861886925068638906788872192
)
-(cos(t5)*(81129638414606676728031405122553*sin(t2-
t1+t3+t4)-81129638414606686663546605165575*sin(t1
+ t2 + t3 +
t4)))/162259276829213363391578010288128,sin(t5)*((
81129638414606676728031405122553*sin(t2
- t1 + t3 + t4))/162259276829213363391578010288128 -
(81129638414606686663546605165575*sin(t1 + t2 + t3
+t4))/162259276829213363391578010288128) - cos(t5)*(cos(t1) -
(403032377821159498335588895202304015643716683825*cos(t1 + t2 + t3
+t4))/1316403645856964833723975346045880403986188692506863890678887219
2
+ (403032377821159448978357750059338280708391237583*cos(t2 - t1 + t3
+t4))/13164036458569648337239753460458804039861886925068638906788872192)
,(81129638414606676728031405122553*cos(t2 - t1
+ t3 + t4))/162259276829213363391578010288128 -
(4967757600021511*cos(t1))/81129638414606681695789005144064
- (81129638414606686663546605165575*cos(t1 + t2
+ t3 +
t4))/162259276829213363391578010288128,(730166
745731460090552282646102977*sin(t1
- t2))/162259276829213363391578010288128
+(730166745731460179971919446490175*sin(t1
+t2+t3))/162259276829213363391578010288128
-(730166745731460090552282646102977*sin(t2-t1 +
t3))/162259276829213363391578010288128 -
(2028240960365167166588665129139375*cos(t1+t2
+ t3 + t4))/649037107316853453566312041152512
+ (730166745731460179971919446490175*sin(t1
+ t2))/162259276829213363391578010288128 -
(124193940000537775*cos(t1))/324518553658426726783156020576256
+ (2028240960365166918200785128063825*cos(t2 - t1 + t3
+t4))/649037107316853453566312041152512]
[

10. 1
0
sin(t2 + t3 + t4)*cos(t5) + sin(t5)*((4967757600021511*cos(t2
+ t3 + t4))/81129638414606681695789005144064
+4967757600021511/81129638414606681695789005144064)
,
cos(t5)*((4967757600021511*cos(t2
+ t3 + t4))/81129638414606681695789005144064
+4967757600021511/81129638414606681695789005144064)-
sin(t2 + t3 + t4)*sin(t5),
24678615572571482867467662723121/658201822928482416861987673022940201993094346253
- cos(t2 + t3 + t4),
9*sin(t2 + t3) - (25*cos(t2 + t3 + t4))/4 + 9*sin(t2)
+269862747400677790913414945939406099782557996250978784280739957961/2632807291713
9
[
0,
0,
0,
1]

11. 1
1
Rob =
Rhino XR1:: 5 axis, RRRRR, stdDH, slowRNE
+---+-----------+-----------+-----------+-----------+-----------+
| j | theta | d | a | alpha | offset |
+---+-----------+-----------+-----------+-----------+-----------+
| 1| q1| 10.25| 0| 1.5708| 0|
| 2| q2| 0| 9| 0| 0|
| 3| q3| 0| 9| 0| 0|
| 4| q4| 0| 0| 1.5708| 0|
| 5| q5| 6.25| 0| 0| 0|
+---+-----------+-----------+-----------+-----------+-----------+
Warning: floor tiles too small, making them 20.000000 x bigger -
change the size
or disable them

12. 1
2
Published with MATLAB® R2018a