ﻪﭽﺨ ﻪﻟﺎﻘﻣ :
ﺖﻓﺎ 2 / 12 / 90
شﺮ 28 / 3 / 91
رد ﻪﺋارا ﺎﺳ ﻳ ﺖ 30 / 6 /
91
ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ود ﺎﺑ
4−R R R R R′′ ′′ ′ ′ ′′
ﻪﻛ
ﻪﺑ يدازآ ﻪﺟرد يدازآ ﻪﺟرد يﻮﮕﻟا ﺎﺑ
ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ ﺞﻨﭘ زا
ﺖﺳا هﺪﻳدﺮﮔ توﺎﻔﺘﻣ ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ﻪﺳ دﺎﺠﻳا ﺚﻋﺎﺑ و هد .
ﻞﻴﻠﺤﺗ
ﻚﻳ ﻪﻛ ﺖﺳا ترﺎﺒﻋ
يﺮﺒﺟ
و سﻮﻜﻌﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻞﺣ ﺎﺑ ﺞﻳﺎﺘﻧ ﻦﻳا
Forward kinematic problem of two 4 geometric structures and one 4
Abstract- In this paper, the forward kinematic of the special cases of parallel mechanisms that respectively lead to two 4
DOF parallel robots has been studied.
motion patterns of 3T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute joints. The directions of revolute joints have been different
structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate mathematical expression of degree 344, 230 and 8 is indicated the forward kinematic
Also, the results are compared with inverse kinematic problem and simulations and their validity have been confirmed Keywords: P
رﺎﺗ ﻳ ﻪﭽﺨ رد ﻳ ﺖﻓﺎ ﺬﭘ ﻳ شﺮ رد ﻪﺋارا
ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ود ﺎﺑ
4−R R R R R′′ ′′ ′′ ′ ′
و
4 R R R R R′′ ′′ ′ ′ ′′
ﻲﻳﺎﻀﻓ يزاﻮﻣ تﺎﺑر ﻚﻳ و 4
يزاﻮﻣ يﺎﻫ 4
يدازآ ﻪﺟرد هﺮﻴﺠﻧز ﺮﻫ ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ ﺞﻨﭘ زا
ﺖﺳا هﺪﻳدﺮﮔ توﺎﻔﺘﻣ ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ﻪﺳ دﺎﺠﻳا ﺚﻋﺎﺑ و هد ﺪﺷ هداد نﺎﺸﻧ ﺖﻳﺎﻬﻧ رد و ﻪﺘﻓﺮﮔ مﺎﺠﻧا يﺪﻌﺑ ه
ﻚﻳ ﻪﻛ ﺖﺳا
و سﻮﻜﻌﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻞﺣ ﺎﺑ ﺞﻳﺎﺘﻧ ﻦﻳا
يﺪﻌﺑ
Forward kinematic problem of two 4 geometric structures and one 4
P. Varshovi
In this paper, the forward kinematic of the special cases of parallel mechanisms that respectively lead to two 4
DOF parallel robots has been studied.
motion patterns of 3T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute joints. The directions of revolute joints have been different
structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate mathematical expression of degree 344, 230 and 8 is indicated the forward kinematic
Also, the results are compared with inverse kinematic problem and simulations and their validity have been confirmed Parallel Robot,
ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ود ﺎﺑ - 4
ﻪﻟﻮﺳﺎﻣ ﻊﻟﺎﻃ يﺪﻬﻣ 3
ناﺪﻤﻫ
ناﺪﻤﻫ ،ﺎﻨﻴﺳ
d_nade
4 R R R R R 4 R R R R R′′ ′′ ′′ ′ ′،
RUR R -
ﻲﻳﺎﻀﻓ يزاﻮﻣ تﺎﺑر ﻚﻳ و4
مﺰﻴﻧﺎﻜﻣ يور ﺮﺑ هﺪﺷ يزاﻮﻣ يﺎﻫ
و نﺎﺴﻜﻳ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ هﺮﻴﺠﻧز رﺎﻬﭼ زا ﺎﻫ هﺮﻴﺠﻧز ﺮﻫ
ﺖﺳا هﺪﻳدﺮﮔ توﺎﻔﺘﻣ ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ﻪﺳ دﺎﺠﻳا ﺚﻋﺎﺑ و هد ﺪﺷ هداد نﺎﺸﻧ ﺖﻳﺎﻬﻧ رد و ﻪﺘﻓﺮﮔ مﺎﺠﻧا يﺪﻌﺑ
. ﻦﻴﻨﭽﻤﻫ
، و سﻮﻜﻌﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻞﺣ ﺎﺑ ﺞﻳﺎﺘﻧ ﻦﻳا
ﻪﺳ ﻲﺳﺪﻴﻠﻗا يﺎﻀﻓ ،ﻢﻴﻘﺘﺴﻣ يﺪﻌﺑ
Forward kinematic problem of two 4 geometric structures and one 4
P. Varshovi
1- PhD Student 2- Assoc
3- Assis
* P.
In this paper, the forward kinematic of the special cases of parallel mechanisms that respectively lead to two 4
DOF parallel robots has been studied. They are originated from the type synthesis of 4
motion patterns of 3T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute joints. The directions of revolute joints have been different
structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate mathematical expression of degree 344, 230 and 8 is indicated the forward kinematic
Also, the results are compared with inverse kinematic problem and simulations and their validity have been confirmed Robot, 3T1R Motion Pattern, Forward Kinematic Problem,
10 - 119
RUR R
- 4
تﺎﺑر ﻚﻳ و توﺎﻔﺘﻣ UU
R -
،*
ﻪﻟﻮﺳﺎﻣ ﻊﻟﺎﻃ يﺪﻬﻣ
ﻲﻠﻋﻮﺑ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ ي ،ﺎﻨﻴﺳ
ناﺪﻤﻫ
ﻲﻠﻋﻮﺑ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ ناﺪﻤﻫ ،ﺎﻨﻴﺳ
ناﺮﻬﺗ ،ناﺮﻬﺗ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ رﺎﻳدﺎﺘﺳا
4−R R R R R′′ ′ ′ ′′ ′′
مﺎﻧ ﻪﺑ توﺎﻔﺘﻣ ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ود ﺎﺑ يدازآ ﻪﺟرد
RUR
ﺰﺘﻨﺳ مﺎﺠﻧا مﺰﻴﻧﺎﻜﻣ يور ﺮﺑ هﺪﺷ
و نﺎﺴﻜﻳ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ هﺮﻴﺠﻧز رﺎﻬﭼ زا ﺎﻫ ﺖﺳا هﺪﻳدﺮﮔ توﺎﻔﺘﻣ ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ﻪﺳ دﺎﺠﻳا ﺚﻋﺎﺑ و هد
ﺪﺷ هداد نﺎﺸﻧ ﺖﻳﺎﻬﻧ رد و ﻪﺘﻓﺮﮔ مﺎﺠﻧا يﺪﻌﺑ
تﺎﺑر زا ﻚﻳ ﺮﻫ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻦﻴﺒﻣ ﺐﻴﺗﺮﺗ ﻪﺑ ﻲﻣ ﺎﻫ
ﺪﺷﺎﺑ .
ﻚﻴﺗﺎﻤﻨﻴﺳ ،ﻲﻧارود ﻪﺟرد ﻪﺳ ﻲﺳﺪﻴﻠﻗا يﺎﻀﻓ ،ﻢﻴﻘﺘﺴﻣ
Forward kinematic problem of two 4 geometric structures and one 4
P. Varshovi Jaghargh1
Student, Mech. Eng., Bu oc. Prof., Mech. Eng.,
Assis. Prof., Mech. Eng., P. O. B. 65175-4161
In this paper, the forward kinematic of the special cases of parallel mechanisms that respectively lead to two 4-R
They are originated from the type synthesis of 4
motion patterns of 3T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute joints. The directions of revolute joints have been different
structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate mathematical expression of degree 344, 230 and 8 is indicated the forward kinematic
Also, the results are compared with inverse kinematic problem and simulations and their validity have been confirmed Motion Pattern, Forward Kinematic Problem,
هرﺎﻤﺷ 4 نﺎﺑآ 1391 ص ص 105
يزاﻮﻣ تﺎﺑر ود ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ RUR
تﺎﺑر ﻚﻳ و توﺎﻔﺘﻣ
يردﺎﻧ دواد
2
*
ﻲﻠﻋﻮﺑ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ ي ﻲﻠﻋﻮﺑ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ ناﺮﻬﺗ ،ناﺮﻬﺗ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ رﺎﻳدﺎﺘﺳا
ﻲﺘﺴﭘ قوﺪﻨﺻ 4161
- 65175
،
مﺰﻴﻧﺎﻜﻣ زا يزاﻮﻣ يﺎﻫ
4 R R R R R′′ ′ ′ ′′ ′′
مﺎﻧ ﻪﺑ توﺎﻔﺘﻣ ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ود ﺎﺑ يدازآ ﻪﺟرد ﻞﺻﺎﺣ ﺎﻫ
ﺰﺘﻨﺳ
تﺎﺑر ﻦﻳا زا ﻚﻳ ﺮﻫ و نﺎﺴﻜﻳ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ هﺮﻴﺠﻧز رﺎﻬﭼ زا ﺎﻫ
ﻮﺑ توﺎﻔﺘﻣ ﺮﮕﻳﺪﻜﻳ ﺎﺑ تﺎﺑر ﻪﺳ ﻦﻳا رد ﻲﻳﻻﻮﻟ ﻞﺻﺎﻔﻣ يﺎﺘﺳار ﺖﺳا هﺪﻳدﺮﮔ توﺎﻔﺘﻣ ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ﻪﺳ دﺎﺠﻳا ﺚﻋﺎﺑ و هد
ﻪﺳ ﻲﺳﺪﻴﻠﻗا يﺎﻀﻓ رد ﺪﺷ هداد نﺎﺸﻧ ﺖﻳﺎﻬﻧ رد و ﻪﺘﻓﺮﮔ مﺎﺠﻧا يﺪﻌﺑ
تﺎﺑر زا ﻚﻳ ﺮﻫ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻦﻴﺒﻣ ﺐﻴﺗﺮﺗ ﻪﺑ ﻚﻴﺗﺎﻤﻨﻴﺳ ،ﻲﻧارود ﻪﺟرد
Forward kinematic problem of two 4 geometric structures and one 4
1, D. Naderi
, Mech. Eng., Bu-Ali Sina Univ., Hamedan Mech. Eng., Bu-Ali Sina Univ., Hamedan Mech. Eng., Tehran Univ., Tehran, Iran
4161 Hamedan,
In this paper, the forward kinematic of the special cases of
RRUR with different geometric structures and one 4 They are originated from the type synthesis of 4
motion patterns of 3T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute joints. The directions of revolute joints have been different with each others that create three different geometrical structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate mathematical expression of degree 344, 230 and 8 is indicated the forward kinematic
Also, the results are compared with inverse kinematic problem and simulations and their validity have been confirmed Motion Pattern, Forward Kinematic Problem,
هرود 12 هرﺎﻤﺷ
يزاﻮﻣ تﺎﺑر ود ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ تﺎﺑر ﻚﻳ و توﺎﻔﺘﻣ
قﺮﻏﺎﺟ يﻮﺷرو مﺎﻴﭘ ،1
يردﺎﻧ دواد
ﺮﺘﻛد يﻮﺠﺸﻧا ا
ﻲﻠﻋﻮﺑ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ ي
- رﺎﻴﺸﻧاد ﻲﻠﻋﻮﺑ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ
3 - ناﺮﻬﺗ ،ناﺮﻬﺗ هﺎﮕﺸﻧاد ،ﻚﻴﻧﺎﻜﻣ ﻲﺳﺪﻨﻬﻣ رﺎﻳدﺎﺘﺳا
،ناﺪﻤﻫ ﻲﺘﺴﭘ قوﺪﻨﺻ
ﻲﺻﺎﺧ ﺖﻟﺎﺣ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ،ﻪﻟﺎﻘﻣ ﻦﻳا رد مﺰﻴﻧﺎﻜﻣ زا
مﺎﻧ ﻪﺑ توﺎﻔﺘﻣ ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ود ﺎﺑ يدازآ ﻪﺟرد
ﺖﺳا ﻪﺘﻓﺮﮔ راﺮﻗ ﻪﻌﻟﺎﻄﻣ درﻮﻣ ،ﺪﻧا .
تﺎﺑر ﻦﻳا ﻞﺻﺎﺣ ﺎﻫ
ﺪﻨﺷﺎﺑ . تﺎﺑر ﻦﻳا زا ﻚﻳ ﺮﻫ
ﻮﺑ توﺎﻔﺘﻣ ﺮﮕﻳﺪﻜﻳ ﺎﺑ تﺎﺑر ﻪﺳ ﻦﻳا رد ﻲﻳﻻﻮﻟ ﻞﺻﺎﻔﻣ يﺎﺘﺳار ﻪﺳ ﻲﺳﺪﻴﻠﻗا يﺎﻀﻓ رد
تﺎﺑر زا ﻚﻳ ﺮﻫ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻦﻴﺒﻣ ﺐﻴﺗﺮﺗ ﻪﺑ
ﺖﺳا هﺪﻴﺳر تﺎﺒﺛا ﻪﺑ نآ ﺖﺤﺻ و هﺪﺷ ﻪﺴﻳﺎﻘﻣ يزﺎﺳ .
و ﻲﻟﺎﻘﺘﻧا ﻪﺟرد 1
ﻚﻴﺗﺎﻤﻨﻴﺳ ،ﻲﻧارود ﻪﺟرد
Forward kinematic problem of two 4-R
geometric structures and one 4-RUU parallel robots
D. Naderi2*, M. Tale
Ali Sina Univ., Hamedan Ali Sina Univ., Hamedan Tehran Univ., Tehran, Iran
In this paper, the forward kinematic of the special cases of 4 R R R R R− ′′ ′ ′ ′′ ′′
RUR with different geometric structures and one 4 They are originated from the type synthesis of 4
motion patterns of 3T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute with each others that create three different geometrical structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate mathematical expression of degree 344, 230 and 8 is indicated the forward kinematic
Also, the results are compared with inverse kinematic problem and simulations and their validity have been confirmed Motion Pattern, Forward Kinematic Problem, Three-Dimensional
يزاﻮﻣ تﺎﺑر ود ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ تﺎﺑر ﻚﻳ و توﺎﻔﺘﻣ
قﺮﻏﺎﺟ يﻮﺷرو مﺎﻴﭘ
1 - د ﺮﺘﻛد يﻮﺠﺸﻧا
2 -
* ،ناﺪﻤﻫ
ﻲﺻﺎﺧ ﺖﻟﺎﺣ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ،ﻪﻟﺎﻘﻣ ﻦﻳا رد ﻲﻳﺎﻀﻓ يزاﻮﻣ تﺎﺑر ود 4
مﺎﻧ ﻪﺑ توﺎﻔﺘﻣ ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ود ﺎﺑ يدازآ ﻪﺟرد
ﺖﺳا ﻪﺘﻓﺮﮔ راﺮﻗ ﻪﻌﻟﺎﻄﻣ درﻮﻣ ،ﺪﻧا ﻲﻧارود ﻪﺟرد ﻲﻣ
ﺪﻨﺷﺎﺑ
ﻮﺑ توﺎﻔﺘﻣ ﺮﮕﻳﺪﻜﻳ ﺎﺑ تﺎﺑر ﻪﺳ ﻦﻳا رد ﻲﻳﻻﻮﻟ ﻞﺻﺎﻔﻣ يﺎﺘﺳار
تﺎﺑر ﻦﻳا ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ يزاﻮﻣ يﺎﻫ
ﻪﺳ ﻲﺳﺪﻴﻠﻗا يﺎﻀﻓ رد
و 8 تﺎﺑر زا ﻚﻳ ﺮﻫ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻦﻴﺒﻣ ﺐﻴﺗﺮﺗ ﻪﺑ
ﺖﺳا هﺪﻴﺳر تﺎﺒﺛا ﻪﺑ نآ ﺖﺤﺻ و هﺪﺷ ﻪﺴﻳﺎﻘﻣ يزﺎﺳ ﻲﺘﻛﺮﺣ يﻮﮕﻟا ،ﻲﻳﺎﻀﻓ يزاﻮﻣ تﺎﺑر 3
و ﻲﻟﺎﻘﺘﻧا ﻪﺟرد
RRUR with different UU parallel robots
M. Tale Masouleh
Ali Sina Univ., Hamedan, Iran Ali Sina Univ., Hamedan, Iran Tehran Univ., Tehran, Iran
4 R R R R R′′ ′ ′ ′′ ′′, 4 R R R R R− ′′ ′′ ′′ ′ ′ RUR with different geometric structures and one 4
They are originated from the type synthesis of 4-DOF parallel mechanisms with motion patterns of 3T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute with each others that create three different geometrical structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate mathematical expression of degree 344, 230 and 8 is indicated the forward kinematic problem of each parallel robot.
Also, the results are compared with inverse kinematic problem and simulations and their validity have been confirmed Dimensional Euclidean
يزاﻮﻣ تﺎﺑر ود ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ
ﻲﺻﺎﺧ ﺖﻟﺎﺣ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ،ﻪﻟﺎﻘﻣ ﻦﻳا رد
ﻪﺑ ﺮﺠﻨﻣ ﺐﻴﺗﺮﺗ ﻪﺑ ﻲﻳﺎﻀﻓ يزاﻮﻣ تﺎﺑر ود
هﺪﻳدﺮﮔ ﺖﺳا ﻪﺘﻓﺮﮔ راﺮﻗ ﻪﻌﻟﺎﻄﻣ درﻮﻣ ،ﺪﻧا
و ﻲﻟﺎﻘﺘﻧا ﻪﺟرد 1
ﻲﻧارود ﻪﺟرد
ﺖﺳا هﺪﺷ ﻞﻴﻜﺸﺗ .
ﻮﺑ توﺎﻔﺘﻣ ﺮﮕﻳﺪﻜﻳ ﺎﺑ تﺎﺑر ﻪﺳ ﻦﻳا رد ﻲﻳﻻﻮﻟ ﻞﺻﺎﻔﻣ يﺎﺘﺳار
تﺎﺑر ﻦﻳا ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻪﺟرد ز 344 ، 230 و
ﺖﺳا هﺪﻴﺳر تﺎﺒﺛا ﻪﺑ نآ ﺖﺤﺻ و هﺪﺷ ﻪﺴﻳﺎﻘﻣ يزﺎﺳ ﻲﺘﻛﺮﺣ يﻮﮕﻟا ،ﻲﻳﺎﻀﻓ يزاﻮﻣ تﺎﺑر
with different UU parallel robots
Masouleh3
4 R R R R R′′ ′′ ′′ ′ ′and 4 R R R R R RUR with different geometric structures and one 4-R
DOF parallel mechanisms with motion patterns of 3T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute with each others that create three different geometrical structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate oblem of each parallel robot.
Also, the results are compared with inverse kinematic problem and simulations and their validity have been confirmed Euclidean Space
يزاﻮﻣ تﺎﺑر ود ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ
هﺪﻴﻜﭼ - ﻲﺻﺎﺧ ﺖﻟﺎﺣ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ،ﻪﻟﺎﻘﻣ ﻦﻳا رد
ﻪﺑ ﺮﺠﻨﻣ ﺐﻴﺗﺮﺗ ﻪﺑ مﺎﻧ
UU R -
هﺪﻳدﺮﮔ 4
ﻲﺘﻛﺮﺣ 3 و ﻲﻟﺎﻘﺘﻧا ﻪﺟرد
ﺖﺳا هﺪﺷ ﻞﻴﻜﺸﺗ ﺴﻣ ﻪﻠﺌ تﺎﺑر ﻦﻳا ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ
ﻚﺗ ا هﺮﻴﻐﺘﻣ ﻪﺟرد ز
ﻪﻴﺒﺷ ﺖﺳا هﺪﻴﺳر تﺎﺒﺛا ﻪﺑ نآ ﺖﺤﺻ و هﺪﺷ ﻪﺴﻳﺎﻘﻣ يزﺎﺳ
ﺪﻴﻠﻛ نﺎﮔژاو : ﻲﺘﻛﺮﺣ يﻮﮕﻟا ،ﻲﻳﺎﻀﻓ يزاﻮﻣ تﺎﺑر
with different UU parallel robots
4 R R R R R− ′′ ′′ ′ ′ ′′
RUU spatial 4- DOF parallel mechanisms with motion patterns of 3T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute with each others that create three different geometrical structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate oblem of each parallel robot.
Also, the results are compared with inverse kinematic problem and simulations and their validity have been confirmed.
هﺪﻴﻜﭼ ﻪﺑ ﺮﺠﻨﻣ ﺐﻴﺗﺮﺗ ﻪﺑ مﺎﻧ ﻲﺘﻛﺮﺣ ﺖﺳا هﺪﺷ ﻞﻴﻜﺸﺗ ﺴﻣ ﻚﺗ ﻪﻴﺒﺷ ﺪﻴﻠﻛ
with different
4 R R R R R′′ ′′ ′ ′ ′′
- DOF parallel mechanisms with motion patterns of 3T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute with each others that create three different geometrical structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate oblem of each parallel robot.
[ Downloaded from mme.modares.ac.ir on 2022-10-31 ]
1 - ﻪﻣﺪﻘﻣ
يزاﻮﻣ تﺎﺑر ﻪﺘﺴﺑ ﻪﻘﻠﺣ مﺰﻴﻧﺎﻜﻣ
يﻮﻜﺳ نآ رد ﻪﻛ ﺖﺳا يا
كﺮﺤﺘﻣ ﻪﺑ يﻮﻜﺳ ﻪﺑ يﺮﺳ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ هﺮﻴﺠﻧز ود ﻞﻗاﺪﺣ ﻪﻠﻴﺳو
ﺖﺳا هﺪﺷ ﻞﺼﺘﻣ ﺖﺑﺎﺛ .
مﺰﻴﻧﺎﻜﻣ ﻦﻳا يﺮﺗﺮﺑ ياراد ﺎﻫ
ﻞﻴﺒﻗ زا ﻲﻳﺎﻫ
رد ﻻﺎﺑ نزو ﻪﺑ وﺮﻴﻧ ﻞﻤﺤﺗ ﺖﺒﺴﻧ و ﺖﻗد ،ﺖﻴﺒﻠﺻ ﺎﺑ ﻪﺴﻳﺎﻘﻣ
تﺎﺑر يﺎﻫ يﺮﺳ ﺘﺴﻫ ﺪﻨ 1] .[ تﺎﺑر رد يزاﻮﻣ يﺎﻫ ﺪﻨﭼ
،ﺮﻴﺧا ﻪﻫد
ﻪﺑ ناﺮﮕﺸﻫوﮋﭘ زا يرﺎﻴﺴﺑ ﻪﺟﻮﺗ درﻮﻣ ،دﺎﻳز رﺎﻴﺴﺑ دﺮﺑرﺎﻛ ﻞﻴﻟد
ﻪﺘﻓﺮﮔ راﺮﻗ ﺖﺳا
. ﻪﻴﺒﺷ زاوﺮﭘ زﺎﺳ 2]
، 3 ﻦﻴﺷﺎﻣ و راﺰﺑا ،[ تﻻآ
3] ،[
تﺎﺑوروﺮﻜﻴﻣ تﺎﺑرﻮﻧﺎﻧ و ﺎﻫ
ﺎﻫ 4] نآ يﺎﻫدﺮﺑرﺎﻛ ﻪﻠﻤﺟ زا [ ﺎﻫ
ﻲﻣ بﻮﺴﺤﻣ ﺪﻧﻮﺷ
. ﻚﭼﻮﻛ يرﺎﻛ يﺎﻀﻓ ﻦﻴﻨﭽﻤﻫ ﻪﺑ ﺖﺒﺴﻧ ﺮﺗ
تﺎﺑر ﻦﻴﻜﺗ طﺎﻘﻧ دﺪﻌﺗ و ﻲﻳﺎﻬﻧ يﺮﺠﻣ هﺪﻴﭽﻴﭘ لﺮﺘﻨﻛ ،يﺮﺳ يﺎﻫ
تﺎﺑر عﻮﻧ ﻦﻳا ﺐﻳﺎﻌﻣ زا يرﺎﻛ يﺎﻀﻓ ﻞﺧاد رد ﻪﺑ ﺎﻫ
بﺎﺴﺣ
ﻲﻣ ﺪﻨﻳآ 1] .[ ﺘﺸﻴﺑ ،زوﺮﻣا ﻪﺑ ﺎﺗ مﺎﺠﻧا ﻲﻠﻤﻋ و يرﻮﺌﺗ يﺎﻫرﺎﻛ ﺮ
هﺪﺷ يور ﺮﺑ
تﺎﺑر يزاﻮﻣ يﺎﻫ 3
ﻪﺤﻔﺻ يدازآ ﻪﺟرد ﺎﻳ و يا
6 ﻪﺟرد يدازآ
ﺖﺳا ﻪﺘﻓﺮﮔ مﺎﺠﻧا .
ﺎﻣا
، لﺎﺳ رد تﺎﺑر ،ﺮﻴﺧا يﺎﻫ ﺎﺑ يزاﻮﻣ يﺎﻫ
زا ﺮﺘﻤﻛ يدازآ ﻪﺟرد 6
) تﺎﺑر يدازآ ﻪﺟرد ﺎﺑ يزاﻮﻣ يﺎﻫ
دوﺪﺤﻣ (1
ﺖﺳا ﻪﺘﻓﺮﮔ راﺮﻗ ﻪﺟﻮﺗ درﻮﻣ 5]
.[ تﺎﺑر عﻮﻧ ﻦﻳا رد ﺎﻫ
تﺎﺑر ﺎﺑ ﻪﺴﻳﺎﻘﻣ يزاﻮﻣ يﺎﻫ
6 يﺮﺗﺮﺑ ياراد يدازآ ﻪﺟرد زا ﻲﻳﺎﻫ
ﻳرﻮﮕﻟا و ﻲﻜﻴﻧﺎﻜﻣ رﺎﺘﺧﺎﺳ ﻞﻴﺒﻗ هدﺎﺳ لﺮﺘﻨﻛ ﻢﺘ
ﺖﺧﺎﺳ ﻪﻨﻳﺰﻫ ،ﺮﺗ
ﻦﻴﻳﺎﭘ ﻲﻣ ﺮﺗﻻﺎﺑ ﺖﻛﺮﺣ ﺖﻋﺮﺳ و ﺮﺗ ﺪﻨﺷﺎﺑ
6] .[ ﻦﻳاﺮﺑﺎﻨﺑ
، نآ رد
تﺎﺑر ﻪﺑ زﺎﻴﻧ ﻪﻛ ﻲﺘﻌﻨﺻ يﺎﻫدﺮﺑرﺎﻛ زا ﻪﺘﺳد ﺎﺑ ﻲﻳﺎﻫ
6 ﻪﺟرد
ﻲﻤﻧ يدازآ تﺎﺑر زا ،ﺪﺷﺎﺑ
يﺎﻫ 4 و 5 هدﺎﻔﺘﺳا يدازآ ﻪﺟرد
ﻲﻣ دﻮﺷ . تﺎﺑر عﻮﻧ ﻦﻳا ﻲﻣ ﺎﻫ
ﻪﺑ ﺪﻨﻧاﻮﺗ ﻦﻴﺷﺎﻣ رد ﺐﻴﺗﺮﺗ راﺰﺑا يﺎﻫ
ﻲﺳ نا
2ﻲﺳ ﺪﻧﺮﻴﮔ راﺮﻗ هدﺎﻔﺘﺳا درﻮﻣ تﺎﻌﻄﻗ ژﺎﺘﻧﻮﻣ و .
ﻦﻴﻟوا
يزاﻮﻣ تﺎﺑر 4
يدازآ ﻪﺟرد
، هﺮﻴﺠﻧز ﺎﺑ ﻜﻴﺗﺎﻤﻨﻴﺳ يﺎﻫ ﻲ
،نﺎﺴﻜﻳ
فﻮﻧﺎﺗﻻز ﻂﺳﻮﺗ 5]
تﺎﺑر نآ زا ﺲﭘ و ﺪﺷ ﻪﺋارا [ يزاﻮﻣ يﺎﻫ
4
ﺪﻳدﺮﮔ ﻪﺋارا يﺮﮕﻳد يدازآ ﻪﺟرد .
فوﺮﻌﻣ زا ﻲﻜﻳ تﺎﺑر ﻦﻳﺮﺗ
يﺎﻫ
يزاﻮﻣ 4 ﺎﺘﻟد تﺎﺑر ،يدازآ ﻪﺟرد ﻲﻣ3
نآ ﻪﻴﻟوا حﺮﻃ ﻪﻛ ﺪﺷﺎﺑ
لوﻼﻛ ﻂﺳﻮﺗ 7]
ﺪﻳدﺮﮔ ﻪﺋارا [ .
ﻢﻬﻣ تﺎﺑر ﻦﻳا ﺖﻳﺰﻣ ﻦﻳﺮﺗ ﺖﻋﺮﺳ
ﻲﻣ نآ ﺖﻛﺮﺣ ﻲﻣ ﻪﻛ ﺪﺷﺎﺑ
تﺎﻛﺮﺣ ﻪﺑ زﺎﻴﻧ ﺎﺑ ﻲﻳﺎﻫدﺮﺑرﺎﻛ رد ﺪﻧاﻮﺗ
دﺮﻴﮔ راﺮﻗ هدﺎﻔﺘﺳا درﻮﻣ ﻊﻳﺮﺳ .
تﺎﺑر ﺮﺜﻛا ﺰﺘﻨﺳ ﻲﻌﺳ سﺎﺳا ﺮﺑ يزاﻮﻣ يﺎﻫ
و و ﺎﻄﺧ
ترﺎﻬﻣ ﺎﻣا ،ﺖﺳا هﺪﺷ مﺎﺠﻧا ﻲﺳﺪﻨﻬﻣ يﺎﻫ شور ًاﺮﻴﺧا
يﺎﻫ
1. Limited-DOF
2. Computer Numerical Control (CNC) 3. DELTA parallel robot
ﺶﭽﻴﭘ يرﻮﺌﺗ ﻞﻴﺒﻗ زا ﻲﻜﻴﺗﺎﻤﺘﺴﻴﺳ ]4
8 ﺮﻴﻴﻐﺗ ﻲﻫوﺮﮔ يرﻮﺌﺗ ،[
5نﺎﻜﻣ 9] يزﺎﺠﻣ هﺮﻴﺠﻧز شور و [ ]6
10 ﻪﻛ ﺖﺳا هﺪﺷ ﻪﺋارا [
ﻲﻣ تﺎﺑر عاﻮﻧا ﺪﻧاﻮﺗ صﺎﺧ ﻲﺘﻛﺮﺣ يﺎﻫﻮﮕﻟا ﺎﺑ ار يزاﻮﻣ يﺎﻫ
ﺪﻨﻛ دﺎﺠﻳا .
ﻲﺘﻛﺮﺣ يﻮﮕﻟا ﻪﻋﻮﻤﺠﻣ ،7
ﺖﻴﻌﻗﻮﻣ زا يا و ﺎﻫ
ﺖﻬﺟ يﺮﻴﮔ ﻪﺘﺳﻮﻴﭘ يﺎﻫ ﺖﺳا يا
ﺖﻛﺮﺣ عاﻮﻧا ﻪﻛ هاﻮﺨﻟد يﺎﻫ
ﺗ ار ﻲﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ ﻲﻣ ﺢﻳﺮﺸ
ﺪﻨﻛ . مﺎﺠﻧا تﺎﻌﻟﺎﻄﻣ ﺮﺜﻛا ﻪﺑ ﺎﺗ هﺪﺷ
مﺰﻴﻧﺎﻜﻣ ﻦﻳا ﺰﺘﻨﺳ يور ﺮﺑ زوﺮﻣا يﺮﺘﻤﻛ ﻪﺟﻮﺗ و هﺪﺷ مﺎﺠﻧا ﺎﻫ
نآ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ ﻞﻴﻠﺤﺗ ﻪﺑ ﺖﺳا هﺪﺷ ﺎﻫ
. شرﺎﻜﻤﻫ و ﮓﻨﻛ 11]
، [
ﺰﺘﻨﺳ ،يزﺎﺠﻣ هﺮﻴﺠﻧز شور و ﺶﭽﻴﭘ يرﻮﺌﺗ سﺎﺳا ﺮﺑ
مﺰﻴﻧﺎﻜﻣ ﺪﻧداد مﺎﺠﻧا ار صﺎﺧ ﻲﺘﻛﺮﺣ يﺎﻫﻮﮕﻟا ﺎﺑ يزاﻮﻣ يﺎﻫ .
نآ مﺰﻴﻧﺎﻜﻣ ﺎﻫ هﺮﻴﺠﻧز ﺎﺑ يدازآ ﻪﺟرد رﺎﻬﭼ يﺎﻫ
ﻲﻜﻴﺗﺎﻤﻨﻴﺳ يﺎﻫ
ﻮﮕﻟا ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ،ار نﺎﺴﻜﻳ ﻪﺳ ﻪﺑ ،كﺮﺤﺘﻣ يﻮﻜﺳ ﻲﺘﻛﺮﺣ ي
ﻪﺘﺳد ﻲﻧارود ﻪﺟرد ﻚﻳ و ﻲﻟﺎﻘﺘﻧا ﻪﺟرد ﻪﺳ
83T1R ود ،
ﻲﻧارود ﻪﺟرد ود و ﻲﻟﺎﻘﺘﻧا ﻪﺟرد
92T2R ﭽﻤﻫ و ﻪﺟرد ﻪﺳ ﻦﻴﻨ
ﻲﻟﺎﻘﺘﻧا ﻪﺟرد ﻚﻳ و ﻲﻧارود
103R1T ﺪﻧدﺮﻛ ﻢﻴﺴﻘﺗ .
ﺰﺘﻨﺳ رد
مﺎﺠﻧا ﺮﻫ رد تﻻﺎﺼﺗا ﻦﻴﺑ ﻲﺳﺪﻨﻫ ﻂﺑاور و عﻮﻧ ،داﺪﻌﺗ ﺎﻬﻨﺗ ،هﺪﺷ
ﺖﺳا هﺪﺷ ﺺﺨﺸﻣ هﺮﻴﺠﻧز .
ﺖﻛﺮﺣ ﺖﻛﺮﺣ ًﺎﺣﻼﻄﺻا ار3T1R
ﺰﻴﻠﻔﻧﻮﺷ ﺖﻛﺮﺣ ﺎﻳ11
ارﺎﻜﺳا ]12
12 ﻲﻣ [ ﺪﻨﻣﺎﻧ . ﻞﻣﺎﺷ ﺖﻛﺮﺣ ﻦﻳا
هوﻼﻋ ﻪﺑ ﻲﻟﺎﻘﺘﻧا ﻪﺟرد ﻪﺳ 1
ﺎﺑ يرﻮﺤﻣ لﻮﺣ ﻲﻧارود ﻪﺟرد
ﻲﻣ ﺖﺑﺎﺛ يﺎﺘﺳار ﺪﺷﺎﺑ
.
هار زا ﻲﻜﻳ زاﻮﻣ تﺎﺑر لﺮﺘﻨﻛ يﺎﻫ
سﺎﺳا ﺮﺑ تﺎﺑر لﺮﺘﻨﻛ ،ي
ﻪﻠﺌﺴﻣ ﻞﺣ ﺖﺳا ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ
. ﻪﻠﺌﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ
ﻢﻴﻘﺘﺴﻣ يزاﻮﻣ تﺎﺑر ﻚﻳ13
اﺪﻴﭘ ﻞﻣﺎﺷ ﺖﻟﺎﺣ ﻲﻣﺎﻤﺗ ندﺮﻛ
يﺎﻫ
ﻤﻋ ﻦﻜﻤﻣ يدورو يازا ﻪﺑ ،ﻲﻳﺎﻬﻧ ﺮﮕﻠ
مﻮﻠﻌﻣ يﺎﻫ
، ﻞﺻﺎﻔﻣ ياﺮﺑ
ﻲﻣ لﺎﻌﻓ ﺪﺷﺎﺑ . ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ترﺎﺒﻋ ،ﻦﻳا ﺮﺑ هوﻼﻋ ﺰﻴﻧ14
هﺮﻴﺠﻧز ﻚﻳ ﺖﻴﻌﺿو ﻲﺿﺎﻳر ترﻮﺻ ﻪﺑ ﻪﻛ ﺖﺳا ﻲﺗرﺎﺒﻋ لﺎﻌﻓ ﻞﺼﻔﻣ ﺖﻴﻌﻗﻮﻣ ﺎﺑ ﺐﺳﺎﻨﺘﻣ ار يزاﻮﻣ تﺎﺑر زا ﻲﻜﻴﺗﺎﻤﻨﻴﺳ ﻲﻣ ﺺﺨﺸﻣ نآ ﺪﻨﻛ
13] .[ ﻪﺘﺳد ﻦﻳا ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻞﻴﻠﺤﺗ
زا تﺎﺑر ﻲﻣ ﻲﺒﺳﺎﻨﻣ ﻲﺿﺎﻳر بﻮﭼرﺎﻬﭼ ﺪﻨﻣزﺎﻴﻧ ،ﺎﻫ ﺪﻧاﻮﺘﺑ ﻪﻛ ﺪﺷﺎﺑ
4. Screw theory
5. Displacement group theory 6. Virtual chain approach 7. Motion pattern
8. 3 Translation and 1 Rotation (3T1R) 9. 2 Translation and 2 Rotation (2T2R) 10. 3 Rotation and 1 Translation (3R1T) 11. Schönflies motion
12. SCARA motion
13. Forward Kinematic Problem (FKP) 14. Forward Kinematic Expression (FKE)
[ Downloaded from mme.modares.ac.ir on 2022-10-31 ]
ﺪﻨﻛ ﺢﻳﺮﺸﺗ ﻞﻣﺎﻛ رﻮﻃ ﻪﺑ ار نارود و لﺎﻘﺘﻧا .
ﻲﻣ رﺎﻛ ﻦﻳا ﺎﺑ ﺪﻧاﻮﺗ
دﺮﻴﮔ مﺎﺠﻧا ﻲﺳﺪﻨﻫ ﺮﺒﺟ زا هدﺎﻔﺘﺳا .
فاﺪﻫا ﻪﻌﻟﺎﻄﻣ ﻲﺳﺪﻨﻫ ﺮﺒﺟ
ﻒﻳﺮﻌﺗ ﺑ هﺪﺷ ﻪ ﺪﻨﭼ ﻪﻠﻴﺳو ﻪﻠﻤﺟ
يا يﺎﻫراﺰﺑا زا هدﺎﻔﺘﺳا ﺎﺑ ﺎﻫ
ﻲﻣ يﺮﺒﺟ ﺪﺷﺎﺑ
. ﻨﻫ ﺮﺒﺟ ءﺎﺸﻨﻣ ترﺎﻛد ﻪﺑ ﻲﺳﺪ
ﻲﻣﺮﺑ1
ﻪﻛ ددﺮﮔ
ﺖﺳا هدﺮﻛ ﻪﺋارا ﻪﻨﻴﻣز ﻦﻳا رد نﺎﺸﺧرد ًﻼﻣﺎﻛ هﺪﻳا ود 13]
، 14 :[
1 ( تﺎﺼﺘﺨﻣ زا هدﺎﻔﺘﺳا ﻲﺳﺪﻴﻠﻗا يﺎﻀﻓ رد طﺎﻘﻧ ﺢﻳﺮﺸﺗ ياﺮﺑ
2 ( ﻲﻨﺤﻨﻣ ﻒﻴﺻﻮﺗ يﺮﺒﺟ تﻻدﺎﻌﻣ ﻂﺳﻮﺗ حﻮﻄﺳ و ﺎﻫ
ﻢﺘﺴﻴﺳ ﺖﻓﺮﺸﻴﭘ ﺎﺑ زا هدﺎﻔﺘﺳا نﺎﻜﻣا ،يﺮﺗﻮﻴﭙﻣﺎﻛ يﺎﻫ
يرﻮﺌﺗ ﻢﺘﻳرﻮﮕﻟا و ﺎﻫ ﺖﺳا ﻪﺘﻓﺎﻳ ﺶﻳاﺰﻓا يﺮﺒﺟ يﺎﻫ
.
ﻢﺘﻳرﻮﮕﻟا ،ﺮﻴﺧا ﻪﻫد ود رد شور و ﺎﻫ
ﻞﺣ ياﺮﺑ يدﺎﻳز يﺎﻫ
تﺎﺑر ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻪﻠﺌﺴﻣ ﺖﺳا هﺪﺷ ﻪﺋارا يزاﻮﻣ يﺎﻫ
.
شرﺎﻜﻤﻫ و ﻦﻳﻼﺴﮔ 15]
ﻪﻠﻤﺟﺪﻨﭼ ﻚﻳ ،[ ﻪﺟرد يا
6 نﺎﻴﺑ ياﺮﺑ
ﻪﺤﻔﺻ يزاﻮﻣ تﺎﺑر ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ يا
R P R - ﺑ3 ﻪ ﺖﺳد
ﺪﻧدروآ . ﺰﻴﻧﺎﻜﻣ ود ﻦﻴﻨﭽﻤﻫ هدﺎﺳ م
مﺰﻴﻧﺎﻜﻣ ياﺮﺑ ﺰﻴﻧ هﺪﺷ يزﺎﺳ
ﺪﻳدﺮﮔ ﻪﺋارا رﻮﺑﺬﻣ .
ﻲﺘﺳﻮﻫ 14] ﺖﺷﺎﮕﻧ زا هدﺎﻔﺘﺳا ﺎﺑ ،[
ﺑ رﺎﺑ ﻦﻴﻟوا ﻪﻛ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ ﻪ
،ﺪﺷ ﻲﻓﺮﻌﻣ يدﻮﺘﺳا ﻪﻠﻴﺳو
يزاﻮﻣ تﺎﺑر ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻞﺣ ياﺮﺑ ﻲﻤﺘﻳرﻮﮕﻟا 6
ﻪﺟرد
دﺮﻛ ﻪﺋارا تراﻮﺘﺳا يدازآ .
يﺎﻫﺮﺘﻣارﺎﭘ زا هدﺎﻔﺘﺳا ﺎﺑ ،ﻢﺘﻳرﻮﮕﻟا ﻦﻳا
،يدﻮﺘﺳا ﻪﺳ ﺖﻛﺮﺣ
ﺖﻔﻫ يﺎﻀﻓ ﻚﻳ ﻪﺑ ار يﺪﻌﺑ يﺪﻌﺑ
ﻪﺒﺷ
2ﻲﻀﻴﺑ ﻲﻣ ﺖﺷﺎﮕﻧ دﺮﻛ
. ﻪﻠﻤﺟﺪﻨﭼ ﻚﻳ ﻪﺑ ﻢﺘﻳرﻮﮕﻟا يا
ﻚﺗ هﺮﻴﻐﺘﻣ ﻪﺟرد زا 40 ﻲﻣ نﺎﺸﻧ ﻪﻛ ﺪﻣﺎﺠﻧا ﻪﻛ ﺖﺳا نآ هﺪﻨﻫد
سﻮﮔ تﺎﺑر ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ -
ياراد ﺮﺜﻛاﺪﺣ تراﻮﺘﺳا 40
ﻲﻣ باﻮﺟ ﺪﺷﺎﺑ
.
شرﺎﻜﻤﻫ و ﻲﻳ 16]
ﻪﻛ ﺪﻧداد شزﻮﻣآ ﻲﺒﺼﻋ ﻪﻜﺒﺷ ﻚﻳ [
يزاﻮﻣ تﺎﺑر ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻞﺣ 6
ار تراﻮﺘﺳا يدازآ ﻪﺟرد
يﺎﻄﺧ ﺎﺑ 86
/ 2 ﻲﻠﻴﻣ و ﺮﺘﻣ 8
/ 2 ﻲﻣ مﺎﺠﻧا ﻪﺟرد داد
.
ﺲﻴﻜﻨﻴﻧوﺮﺑ 17]
ﺳ ﻪﺘﺴﺑ ﻞﺣ [ يزاﻮﻣ تﺎﺑر ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴ
ﺖﻧﺎﻫ - اﺪﻴﭘ ﻪﻳﺎﭘ ﺮﺑ ار زوﺮﻤﻳﺮﭘ ﻲﻬﺟورﺎﻬﭼ ﻲﻳﻻﺎﺑ ﻪﻄﻘﻧ ندﺮﻛ
ﻲﻳﺎﻫ
ﺠﻧز ار نآ عﻼﺿا ﻪﻛ هﺮﻴ
ﻲﻣ ﻞﻴﻜﺸﺗ يزاﻮﻣ تﺎﺑر يﺎﻫ ﻪﺋارا ،داد
دﺮﻛ . شرﺎﻜﻤﻫ و ﻲﻟ 18]
تﺎﺑر ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ،ﺰﻴﻧ [
يﺮﺒﺟ فﺬﺣ زا هدﺎﻔﺘﺳا ﺎﺑ ار تراﻮﺘﺳا ﺑ3
ﻪ نﺎﺸﻧ و ﺪﻧدروآ ﺖﺳد
ﻪﻠﻤﺟﺪﻨﭼ ﻚﻳ ﻪﻛ ﺪﻧداد ﻚﺗ يا
ﻪﺟرد زا هﺮﻴﻐﺘﻣ 40
ﺮﮕﻧﺎﻴﺑ
ﻲﻣ تﺎﺑر ﻦﻳا ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﺪﺷﺎﺑ
. و ﻪﻟﻮﺳﺎﻣ ﻊﻟﺎﻃ
ﺶﻧارﺎﻜﻤﻫ 19]
يزاﻮﻣ تﺎﺑر ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ،[ UR
P R - ار 5
1. Descartes
2. Seven-dimensional quasi-elliptic space 3. Algebraic elimination
هدﺎﺳ حﺮﻃ ود و ﻲﺳرﺮﺑ ﻪﺋارا مﺰﻴﻧﺎﻜﻣ ﻦﻳا ياﺮﺑ هﺪﺷ يزﺎﺳ
نآ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻞﻴﻠﺤﺗ ﻪﻛ ﺪﻧدﺮﻛ هدﺎﺳ ﺎﻫ
مﺰﻴﻧﺎﻜﻣ زا ﺮﺗ
ﻲﻣ مﺎﺠﻧا ﻲﻠﺻا يزاﻮﻣ ﺖﻓﺮﮔ
. ﺶﻧارﺎﻜﻤﻫ و وا ،ﻦﻴﻨﭽﻤﻫ 13]
ود[
ﺌﺴﻣ ﻞﺣ ياﺮﺑ شور ﺮﺑ يزاﻮﻣ تﺎﺑر ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻪﻠ
ﺪﻧدﺮﻛ ﻪﺋارا يدﻮﺘﺳا يﺎﻫﺮﺘﻣارﺎﭘ زا هدﺎﻔﺘﺳا ﻪﻳﺎﭘ .
،لوا شور رد
ﻲﻣ فﺬﺣ لﺎﻌﻓﺮﻴﻏ يﺎﻫﺮﻴﻐﺘﻣ ،ﺎﻄﺧ و ﺶﻳﺎﻣزآ سﺎﺳا ﺮﺑ ﺪﻧﺪﺷ
ﻪﻠﻤﺟﺪﻨﭼ ﺪﻴﻟﻮﺗ ﻪﻳﺎﭘ ﺮﺑ ،مود شور رد و يا
ﻲﻄﺧ يﺎﻫ )
هدﺎﻔﺘﺳا
ﻢﺘﻳرﻮﮕﻟا زا
4LIA ( و ﻞﺻﺎﻔﻣ ﻪﺑ طﻮﺑﺮﻣ يﺎﻫﺮﻴﻐﺘﻣ فﺬﺣ
ﺮﻴﻏ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ترﺎﺒﻋ ،لﺎﻌﻓ ﻲﻣ ﻞﺻﺎﺣ
ﺪﺷ . ﻦﻳا رد
ﺗ ،شور ﺖﻳوﺎﻧد يﺎﻫﺮﺘﻣارﺎﭘ ﻪﺋارا ﺎﺑ ﺎﻬﻨ -
،هﺮﻴﺠﻧز ﻚﻳ گﺮﺒﻨﺗرﺎﻫ
ﻲﻣ ﺑ ار ﻲﻜﻴﺗﺎﻤﻨﻴﺳ ترﺎﺒﻋ ناﻮﺗ ﻪ
دروآ ﺖﺳد .
،ﻦﻴﻨﭽﻤﻫ
تﺎﺑر ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ يزاﻮﻣ يﺎﻫ
5 يﻮﮕﻟا ﺎﺑ يدازآ ﻪﺟرد
ﻲﺘﻛﺮﺣ مود شور رد هﺪﺷ ﻪﺋارا ﻢﺘﻳرﻮﮕﻟا ﻂﺳﻮﺗ ﺰﻴﻧ 3R2T
ﺖﻓﺮﮔ راﺮﻗ ﻲﺳرﺮﺑ درﻮﻣ .
ﻪﺟﻮﺗ ﺎﺑ مﺎﺠﻧا تﺎﻘﻴﻘﺤﺗ ﻪﺑ
ﻪﻨﻴﻣز رد هﺪﺷ ﻚﻴﺗﺎﻤﻨﻴﺳ
مﺰﻴﻧﺎﻜﻣ ﻢﻴﻘﺘﺴﻣ ﻪﭽﺨﻳرﺎﺗ ﻞﻴﻟد ﻪﺑ و يزاﻮﻣ يﺎﻫ
تﺎﺑر هﺎﺗﻮﻛ يﺎﻫ
ﻲﻳﺎﻀﻓ يزاﻮﻣ 4
هﺮﻴﺠﻧز رﺎﺘﺧﺎﺳ ﺎﺑ يدازآ ﻪﺟرد ،نﺎﺴﻜﻳ يﺎﻫ
تﺎﺑر زا ﻪﺘﺳد ﻦﻳا ﻲﻜﻴﺗﺎﻤﻨﻴﺳ تﺎﺼﺨﺸﻣ دوﺪﺤﻣ رﺎﻴﺴﺑ ﺎﻫ
ﻲﺳرﺮﺑ هﺪﺷ ﺖﺳا . تﺎﺑر ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ،ﻦﻴﻨﭽﻤﻫ يﺎﻫ
يزاﻮﻣ ﻲﻳﺎﻀﻓ ) ﻪﻠﺻﺎﺣ ﻲﻄﺧﺮﻴﻏ تﻻدﺎﻌﻣ ﻢﺘﺴﻴﺳ ﻞﻴﻟد ﻪﺑ (
،
ﻲﻤﻧ و ﺖﺳا هﺪﻴﭽﻴﭘ ددﺮﮔ ﻞﻴﻠﺤﺗ ﻲﺘﺣار ﻪﺑ ﺪﻧاﻮﺗ
. ،ﻖﻴﻘﺤﺗ ﻦﻳا رد
يزاﻮﻣ تﺎﺑر ﻪﺳ ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ اﺪﺘﺑا 4
يدازآ ﻪﺟرد
RUR1
R - ،4 RUR2
R - و4 UU R - ﻲﺘﻛﺮﺣ يﻮﮕﻟا ﺎﺑ4 3T1R
ﺖﺳا هﺪﺷ ﺢﻳﺮﺸﺗ .
ﻪﻠﺌﺴﻣ ﺲﭙﺳ ﺖﻟﺎﺣ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ
تﺎﺑر ﻦﻳا ﻲﻣﻮﻤﻋ ﺑ ﺎﺗ ﻪﻛ ﺎﻫ
ﻪ ﻪﺘﻓﺮﮕﻧ راﺮﻗ ﻲﺳرﺮﺑ درﻮﻣ لﺎﺣ
ﻚﺗ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ ترﺎﺒﻋ ﻚﻳ و ﺖﺳا هﺪﺷ ﻪﺋارا ،ﺖﺳا هﺮﻴﻐﺘﻣ
، ﻪﻛ
ﮕﻧﺎﻴﺑ ﻲﻣ ﻢﻴﻘﺘﺴﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻪﻠﺌﺴﻣ ﺮ زا ﻚﻳ ﺮﻫ ياﺮﺑ ،ﺪﺷﺎﺑ
تﺎﺑر ﺑ ﺎﻫ ﻪ و سﻮﻜﻌﻣ ﻚﻴﺗﺎﻤﻨﻴﺳ ﻞﺣ ﺞﻳﺎﺘﻧ ﺎﺑ و هﺪﻣآ ﺖﺳد
ﻪﻴﺒﺷ ﺖﺳا هﺪﺷ ﻪﺴﻳﺎﻘﻣ يزﺎﺳ .
نﺎﻳﺎﺷ ﻪﻛ ﺖﺳا ﺮﻛذ ﻦﻳا رد
رد ﻲﻜﻴﻧﺎﻜﻣ ﻞﺧاﺪﺗ ،ﻪﻌﻟﺎﻄﻣ ﺖﺳا هﺪﺸﻧ ﻪﺘﻓﺮﮔ ﺮﻈﻧ
.
2 - تﺎﺑر ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ﻪﺟرد رﺎﻬﭼ يزاﻮﻣ يﺎﻫ
يدازآ (3T1R) ﺮﻈﻧ درﻮﻣ
رد ﻊﺟﺮﻣ 11]
، [ 11 مﺰﻴﻧﺎﻜﻣ 4 ﻲﺘﻛﺮﺣ يﻮﮕﻟا ﺎﺑ يدازآ ﻪﺟرد 3
ﻪﺟرد و ﻲﻟﺎﻘﺘﻧا 1
ﻪﻛ ﺖﺳا هﺪﺷ ﻲﻓﺮﻌﻣ ﻲﻧارود ﻪﺟرد 6
مﺰﻴﻧﺎﻜﻣ
4. Linear Implicitization Algorithm
[ Downloaded from mme.modares.ac.ir on 2022-10-31 ]
نآ زا ﺎﻫ هوﺮﮔ رد ) 5R
زا ﻞﻜﺸﺘﻣ 5
ﺮﻫ رد ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ
هﺮﻴﺠﻧز ( ﻪﻘﺒﻃ هﺪﺷ يﺪﻨﺑ ﺪﻧا
. مﺰﻴﻧﺎﻜﻣ ﻲﻳﺎﻀﻓ يزاﻮﻣ يﺎﻫ
4 R R R R R− ′′ ′ ′ ′′ ′′
،
4 R R R R R− ′′ ′′ ′′ ′ ′
و
4 R R R R R− ′′ ′′ ′ ′ ′′
) ﺲﻳﻮﻧﻻﺎﺑ ﺎﺑ ﻞﺻﺎﻔﻣ ﻲﻣ يزاﻮﻣ يﺎﻫرﻮﺤﻣ ياراد نﺎﺴﻜﻳ
ﺪﻨﺷﺎﺑ (،
نآ ﻲﻠﻛ حﺮﻃ ﻪﻛ ﻪﺑ ﺎﻫ
ﻞﻜﺷ رد ﺐﻴﺗﺮﺗ يﺎﻫ
1 - ،ﻒﻟا 2 - و ﻒﻟا
3 - هوﺮﮔ زا ،ﺖﺳا هﺪﺷ هدروآ ﻒﻟا ﺪﻨﺘﺴﻫ5R
تﺎﺑرو يزاﻮﻣ يﺎﻫ
RUR1
R -
،4 RUR2
R - و4 UU R - )4 ﻞﻜﺷ يﺎﻫ 1 - ،ب 2 - و ب
3 - ب ( ﺰﻴﻧ ﻪﺑ ، مﺰﻴﻧﺎﻜﻣ ﻪﺳ ﻦﻳا زا ﻲﺻﺎﺧ ﺖﻟﺎﺣ ،ﺐﻴﺗﺮﺗ ﻲﻣ
ﺪﻨﺷﺎﺑ .
نﺎﻳﺎﺷ ﺎﺑ ﻲﻳﻻﻮﻟ ﻞﺻﺎﻔﻣ ﻪﻟﺎﻘﻣ ﻦﻳا ﺮﺳﺎﺗﺮﺳ رد ﻪﻛ ﺖﺳا ﺮﻛذ وR
ﺎﺑ لﺎﺳرﻮﻴﻧﻮﻳ ﻞﺻﺎﻔﻣ ﺖﺳا هﺪﺷ هداد نﺎﺸﻧ U
. ﻦﻴﻨﭽﻤﻫ
، ﺮﻳز رد
نآ ﻪﻛ ﺖﺳا هﺪﺷ هﺪﻴﺸﻛ ﻲﻄﺧ لﺎﻌﻓ ﻞﺻﺎﻔﻣ ﻞﺻﺎﻔﻣ زا ار ﺎﻫ
ﻲﻣ اﺰﺠﻣ لﺎﻌﻓﺮﻴﻏ ﺪﻳﺎﻤﻧ
.
نﺎﻤﻫ ﻞﻜﺷ رد ﻪﻛ ﻪﻧﻮﮔ يﺎﻫ
1 - ،ب 2 - و ب 3 - ب هﺪﻫﺎﺸﻣ
ﻲﻣ ،دﻮﺷ ﻚﻳ ﺮﻫ ﻞﻴﻜﺸﺗ ﻲﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ ﻚﻳ زا تﺎﺑر ﻪﺳ ﻦﻳا زا
هﺪﺷ ﻴﺳو ﻪﺑ ﻮﻜﺳ ﻦﻳا ﻪﻛ ﺪﻧا هﺮﻴﺠﻧز رﺎﻬﭼ ﺔﻠ
نﺎﺴﻜﻳ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ
هﺪﺷ ﻞﺼﺘﻣ ﺖﺑﺎﺛ يﻮﻜﺳ ﻪﺑ ﺖﺳا
. ﻦﻴﻨﭽﻤﻫ
، ﺑﺎﺛ بﻮﭼرﺎﻬﭼ ﺖ
Oxyz
، ﻞﺼﻔﻣ يور ﺮﺑ B1
) رﻮﺤﻣ ﻪﻛ يرﻮﻃ ﻦﻴﻟوا يﺎﺘﺳار ردz
دﺮﻴﮔ راﺮﻗ لﺎﻌﻓ ﻞﺼﻔﻣ نﺎﻤﻫ ﺎﻳ ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ (
بﻮﭼرﺎﻬﭼ و
كﺮﺤﺘﻣ O′x′y′z′
ﻞﺼﻔﻣ يور ﺮﺑ Ei
) رﻮﺤﻣ يﺎﺘﺳار ﻪﻛ يرﻮﻃ z′
رﻮﺤﻣ يﺎﺘﺳار رد دﺮﻴﮔ راﺮﻗ ﺖﺑﺎﺛ بﻮﭼرﺎﻬﭼ زاz
( هداد راﺮﻗ هﺪﺷ
ﺖﺳا . ﺎﺑ ﻪﺟﻮﺗ ﻪﺑ تﺎﺑر ﻦﻳا ﺮﺑ ﻢﻛﺎﺣ دﻮﻴﻗ و ﻂﻳاﺮﺷ ﺖﻬﺟ ،ﺎﻫ
يﺮﻴﮔ
رﻮﺤﻣ رﻮﺤﻣ ﺖﻬﺟ رد و ﺖﺑﺎﺛ هراﻮﻤﻫ ،كﺮﺤﺘﻣ بﻮﭼرﺎﻬﭼ زاz′
z
ﻲﻣ ﺖﺑﺎﺛ بﻮﭼرﺎﻬﭼ زا ﺖﻬﺟ ﺎﻣا ،ﺪﺷﺎﺑ
يﺎﻫرﻮﺤﻣ يﺮﻴﮔ و x′
،y′
يدورو ﺮﻴﻴﻐﺗ ﺎﺑ ﻲﻣ ﺮﻴﻴﻐﺗ ،مﺰﻴﻧﺎﻜﻣ يﺎﻫ
ﺪﻨﻛ . ﺮﻫ ﻲﻳﺎﻬﻧ يﺮﺠﻣ
تﺎﺑر ﻦﻳا زا ﻚﻳ ﻲﻟﺎﻘﺘﻧا ﻪﺟرد ﻪﺳ دﺎﺠﻳا ﻲﻳﺎﻧاﻮﺗ ﺎﻫ
) ،x ،y (z ﻪﺑ
هوﻼﻋ رﻮﺤﻣ لﻮﺣ ﻲﻧارود ﻪﺟرد ﻚﻳ )z
(θ ﻲﻣ اراد ار ﺪﻨﺷﺎﺑ
. رد
ءﺰﺟ تﺎﺑر ﻪﺳ ﻦﻳا ،ﺖﻘﻴﻘﺣ تﺎﺑر
ﻪﺟرد ﺎﺑ يﺎﻫ دوﺪﺤﻣ يدازآ
ﻲﻣ نآ ﻲﻳﺎﻬﻧ يﺮﺠﻣ ﻪﻛ ﺪﻨﺷﺎﺑ ﺎﻫ
ﻲﻤﻧ ﻲﻳﺎﻫرﻮﺤﻣ لﻮﺣ ﺪﻧاﻮﺗ
يﺎﻫرﻮﺤﻣ يزاﻮﻣ و x
ﺪﻨﻛ نارود y .
زاﺪﻧارﺎﻛ ﻚﻳ ،ﻦﻴﻨﭽﻤﻫ
رﻮﺤﻣ يزاﻮﻣ ﻲﻧارود رﻮﺤﻣ ﺎﺑ ﻲﻳﻻﻮﻟ ﺰﻴﻧ z
) يﻮﻜﺳ ﻪﺑ ﻞﺼﺘﻣ
ﺖﺑﺎﺛ ( ورو د ﻲﻣ ﻞﻴﻜﺸﺗ ار هﺮﻴﺠﻧز ﺮﻫ ي ﺪﻫد
. هوﻼﻋ هزاﺪﻧا ،ﻦﻳا ﺮﺑ
ﻪﻳواز هﺮﻴﺠﻧز ﺮﻫ رد ﻲﻳﻻﻮﻟ زاﺪﻧارﺎﻛ )
θi ( ﺖﻬﺟ ﻪﺑ ﺖﺒﺴﻧ هراﻮﻤﻫ
رﻮﺤﻣ ﺖﺒﺜﻣ ﻲﻣ هﺪﻴﺠﻨﺳx
دﻮﺷ .
ﻞﻜﺷ رد يﺎﻫ 4 ، 5 و 6 هﺮﻴﺠﻧز ﻲﻠﻛ حﺮﻃ ،ﺐﻴﺗﺮﺗ ﻪﺑ ،ﺰﻴﻧ يﺎﻫ
ﻲﻜﻴﺗﺎﻤﻨﻴﺳ RUR1
،R RUR2
و R UU هﺪﺷ هداد نﺎﺸﻧR
ﺖﺳا . رادﺮﺑ ri
ﻪﻄﻘﻧ ﺖﻴﻌﻗﻮﻣ رادﺮﺑ ناﻮﻨﻋ ﻪﺑ Bi
) ﻦﻴﻟوا نﺎﻜﻣ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ هﺮﻴﺠﻧز ﺮﻫ رد ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ
( ﺖﺑﺎﺛ بﻮﭼرﺎﻬﭼ رد
ﻲﻣ ﻒﻳﺮﻌﺗ دﻮﺷ
. رادﺮﺑ ،ﻪﺑﺎﺸﻣ رﻮﻃ ﻪﺑ d′i
ﻪﻄﻘﻧ ﺖﻴﻌﻗﻮﻣ رادﺮﺑ ﺰﻴﻧ
Ei
رد بﻮﭼرﺎﻬﭼ كﺮﺤﺘﻣ
) نﺎﻜﻣ ﻦﻳﺮﺧآ ﻞﺼﻔﻣ ﻲﻳﻻﻮﻟ هﺮﻴﺠﻧز رد
هرﺎﻤﺷ (i ﺖﺳا . ﻦﻴﻨﭽﻤﻫ
، هﺮﻴﺠﻧز رد ﻲﻜﻴﺗﺎﻤﻨﻴﺳ يﺎﻫ
RUR1
R
و RUR2
،R هزاﺪﻧا يﺎﻫرادﺮﺑ Ci
Bi
، Di
Ci
و Ei
Di
ﻪﺑ ﺎﺑ ﺐﻴﺗﺮﺗ
ﺮﻳدﺎﻘﻣ ai
، L1
و L2
هﺮﻴﺠﻧز رد و ﻲﻜﻴﺗﺎﻤﻨﻴﺳ
UU هزاﺪﻧا ،R
رادﺮﺑ يﺎﻫ BiCi
و CiEi
ﻪﺑ ﺮﻳدﺎﻘﻣ ﺎﺑ ﺐﻴﺗﺮﺗ ai
و L1
هداد نﺎﺸﻧ
ﻲﻣ ﺪﻧﻮﺷ . ﻲﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ ﺖﻴﻌﻗﻮﻣ ،ﺖﻳﺎﻬﻧ رد )
ﻪﻄﻘﻧ لﺎﺼﺗا رادﺮﺑ
ﻪﻄﻘﻧ ﻪﺑ O O′
ﺑ( ﻪ رادﺮﺑ ﻪﻠﻴﺳو ]T
z , y , x
=[
و p ﺖﻬﺟ يﺮﻴﮔ
كﺮﺤﺘﻣ بﻮﭼرﺎﻬﭼ )
ﻲﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ (
ﺰﻴﻧ ﺖﺑﺎﺛ بﻮﭼرﺎﻬﭼ ﻪﺑ ﺖﺒﺴﻧ
ﺑ ﻪ نارود ﺲﻳﺮﺗﺎﻣ ﻪﻠﻴﺳو )Q
ﻪﻄﺑار 1 ( ﻲﻣ نﺎﻴﺑ ددﺮﮔ .
) 1 ( 0
0
0 0 1
c s
s c
θ θ
θ θ
−
=
Q
،قﻮﻓ ﻂﺑاور رد ﻪﻛ sin
sθ = θ و
cos cθ = θ ﻲﻣ
ﺪﺷﺎﺑ .
ﻦﻴﻨﭽﻤﻫ
، طﺎﻘﻧ ﻪﻛ ﺎﺠﻧآ زا Ei
) هﺮﻴﺠﻧز ﺮﻫ رد ﻲﻳﺎﻬﺘﻧا ﻞﺼﻔﻣ (
ﻪﺑ
ﻲﻣ ،ﺖﺳا ﻞﺼﺘﻣ ﻲﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ ،ار نآ ﺖﻴﻌﻗﻮﻣ ناﻮﺗ
ﻪﺳ ياﺮﺑ
،ﻪﻌﻟﺎﻄﻣ ﺖﺤﺗ يزاﻮﻣ تﺎﺑر ﺖﻴﻌﻗﻮﻣ سﺎﺳا ﺮﺑ ﻢﻴﻘﺘﺴﻣ ترﻮﺻ ﻪﺑ
ﻲﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ )
يﺎﻫﺮﺘﻣارﺎﭘ ،x
،y وz (θ ﺖﺷﻮﻧ :
[
xEi yEi zEi]
T= +p Q d⋅ ′i) 2 ( 0
0
0 0 1
ix iy iz
x c s d
y s c d
z d
θ θ
θ θ
− ′
= + ′
′
ix iy
ix iy
x d c d s
y d s d c
z
θ θ
θ θ
′ ′
+ −
′ ′
= + +
ﻪﻛ رد ﻪﺳ تﺎﺑر يزاﻮﻣ
،قﻮﻓ (0,0,0)
′ =1 ،d
2 ( ,b b, 0)
′ = − ،d
3 (0, 2 , 0)b
′ = − و d
4 ( b, b, 0)
′ = − −
)d
لﻮﻃ ﻒﺼﻧ b
ﻲﻣ ﻲﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ ﺪﺷﺎﺑ
.(
ﻦﻴﻨﭽﻤﻫ
، طﺎﻘﻧ ﺖﻴﻌﻗﻮﻣ Ci
) ﻦﻴﻟوا
هﺮﻴﺠﻧز ﺮﻫ رد لﺎﻌﻓ ﻞﺼﻔﻣ زا ﺲﭘ ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ (
ﻪﺑ ﺖﺒﺴﻧ
ﻲﻣ ار ﺖﺑﺎﺛ بﻮﭼرﺎﻬﭼ دﺮﻛ نﺎﻴﺑ ﺮﻳز ترﻮﺻ ﻪﺑ ناﻮﺗ
:
) 3 (
[ ]
[
cos sin]
T
Ci Ci Ci
T
Bi i Bi i Bi
x y z
x a θ y a θ z
=
+ ⋅ + ⋅
تﺎﺑر ﻦﻳا زا ﻚﻳ ﺮﻫ ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ ﺢﻳﺮﺸﺗ ﻪﺑ ﻪﻣادا رد ﺎﻫ
ﻲﻣ ﻪﺘﺧادﺮﭘ دﻮﺷ
.
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ﻞﻜﺷ ﻒﻟا1 - ﻪﺋارا ﻲﻠﻛ حﺮﻃ ياﺮﺑ هﺪﺷ
تﺎﺑر يزاﻮﻣ 4 R R R R R− ′′ ′ ′ ′′ ′′
] 11 [ ب ، - ﻪﻴﺒﺷ حﺮﻃ مﺮﻧ يزﺎﺳ
يزاﻮﻣ تﺎﺑر يراﺰﻓا RUR1
R - 4
ﻞﻜﺷ ﻒﻟا2 - حﺮﻃ ﻪﺋارا ﻲﻠﻛ يزاﻮﻣ تﺎﺑر ياﺮﺑ هﺪﺷ 4 R R R R R− ′′ ′′ ′′ ′ ′
] 11 [ ب ، - ﻪﻴﺒﺷ حﺮﻃ مﺮﻧ يزﺎﺳ
يزاﻮﻣ تﺎﺑر يراﺰﻓا RUR2
R - 4
ﻞﻜﺷ ﻒﻟا3 - ﻪﺋارا ﻲﻠﻛ حﺮﻃ يزاﻮﻣ تﺎﺑر ياﺮﺑ هﺪﺷ
4 R R R R R− ′′ ′′ ′ ′ ′′
] 11 [ ب ، - ﻪﻴﺒﺷ حﺮﻃ مﺮﻧ يزﺎﺳ
يزاﻮﻣ تﺎﺑر يراﺰﻓا UU
R - 4
ﻒﻟا ب
ﻲﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ
ﺖﺑﺎﺛ يﻮﻜﺳ Ei
y′
y O
i=1 θi x Di
Ci L1
Ai Bi i=2 i=3
z
x′
z′
L2
i=4 O′
a
ب ﻒﻟا
ﻲﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ
ﺖﺑﺎﺛ يﻮﻜﺳ O′
i=3 x
O i=1 Ai Bi z y
i=4 θi Ei
Di Ci L1 i=2
z′
L2 y′
a
x′
ﻲﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ
ﺖﺑﺎﺛ يﻮﻜﺳ x
Ai Bi Ci
L1 z′
y y′
Ei
L2
x′
z O′
O i=1 i=2
i=3
i=4 ﻒﻟا ب
[ Downloaded from mme.modares.ac.ir on 2022-10-31 ]
2 - 1 - يزاﻮﻣ تﺎﺑر ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ RUR1
R - 4
ﻞﺼﻔﻣ ود ﻦﻴﺑ ﻂﺑار فاﺮﺤﻧا و لﻮﻃ ﻪﻛ ﻲﻣﺎﮕﻨﻫ ﺮﻔﺻ ﺮﺑاﺮﺑ ﻲﻳﻻﻮﻟ
نآ ﻂﺑار ﺶﭽﻴﭘ ﻪﻳواز و ﺮﺑاﺮﺑ ﺎﻫ
90 ﻞﺼﻔﻣ ﻚﻳ ،ﺪﺷﺎﺑ ﻪﺟرد
لﺎﺳرﻮﻴﻧﻮﻳ ﻲﻣ ﻞﻴﻜﺸﺗ1
دﻮﺷ 20] .[ يزاﻮﻣ تﺎﺑر RUR1
R - ﺰﻴﻧ 4 ،
يزاﻮﻣ مﺰﻴﻧﺎﻜﻣ زا ﻲﺻﺎﺧ ﺖﻟﺎﺣ 4−R R R R R′′ ′ ′ ′′ ′′
ﻲﻣ ﺪﺷﺎﺑ
ﺮﻫ زا مرﺎﻬﭼ و مﻮﺳ ﻲﻳﻻﻮﻟ ﻞﺻﺎﻔﻣ نارود يﺎﻫرﻮﺤﻣ ،نآ رد ﻪﻛ ﻲﻣ ﻞﻴﻜﺸﺗ ار لﺎﺳرﻮﻴﻧﻮﻳ ﻞﺼﻔﻣ ﻚﻳ هﺮﻴﺠﻧز ﺪﻨﻫد
.
ﻞﻜﺷ 4 حﺮﻃ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ هﺮﻴﺠﻧز ﻲﻠﻛ يزاﻮﻣ تﺎﺑر زا ماi
RUR1
R - ﻲﻣ نﺎﺸﻧ ار4 ﻪﻛ ﺪﻫد
مﺎﺠﻧا ﺰﺘﻨﺳ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ رد هﺪﺷ
ﻊﺟﺮﻣ 11] ﺖﺳا هﺪﺷ دﺎﺠﻳا [ .
ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ ﻚﻳ
،T رﻮﺤﻣ ﺎﺑ
رﻮﺤﻣ يزاﻮﻣ نارود ار هﺮﻴﺠﻧز ﺮﻫ لﺎﻌﻓ ﻞﺼﻔﻣ و يدورو ،z
ﻲﻣ ﻞﻴﻜﺸﺗ ﺪﻫد
. رد مﻮﺳ و مود ﻲﻳﻻﻮﻟ ﻞﺻﺎﻔﻣ نارود يﺎﻫرﻮﺤﻣ
هراﻮﻤﻫ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ هﺮﻴﺠﻧز ﺮﻫ ﻪﺤﻔﺻ رد و يزاﻮﻣ
يزاﻮﻣ يا
ﻪﺤﻔﺻ ﺪﻧراد راﺮﻗ x-y
. ياراد ﺰﻴﻧ ﻲﻳﺎﻬﺘﻧا ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ ود
يﺎﻫرﻮﺤﻣ يزاﻮﻣ
) يزاﻮﻣ رﻮﺤﻣ (z ﻲﻣ ﺪﻨﺷﺎﺑ . ﻦﻴﻨﭽﻤﻫ
، يﺎﻫرﻮﺤﻣ
ﻊﻃﺎﻘﺘﻣ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ هﺮﻴﺠﻧز ﺮﻫ رد مرﺎﻬﭼ و مﻮﺳ ﻞﺻﺎﻔﻣ نارود ﻲﻣ ﻞﻴﻜﺸﺗ ار لﺎﺳرﻮﻴﻧﻮﻳ ﻞﺼﻔﻣ ﻚﻳ و هدﻮﺑ دﻮﻤﻋ ﻢﻫ ﺮﺑ و ﺪﻨﻫد
.
نﺎﻳﺎﺷ يزاﻮﻣ تﺎﺑر رد ﻪﻛ ﺖﺳا ﺮﻛذ RUR1
R - رﺎﻬﭼ 4
ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ رﺎﻬﭼ و ﺖﺑﺎﺛ يﻮﻜﺳ ﻪﺑ ﻞﺼﺘﻣ ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ ﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ ﻪﺑ ﻞﺼﺘﻣ يزاﻮﻣ يﺎﻫرﻮﺤﻣ ياراد هراﻮﻤﻫ ﻲ
) يزاﻮﻣ
رﻮﺤﻣ (z ﻲﻣ ﺪﻨﺷﺎﺑ .
ﻞﻜﺷ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ هﺮﻴﺠﻧز ﻲﻠﻛ حﺮﻃ4 يزاﻮﻣ تﺎﺑر زا ماi
RUR R - 4
1. Universal joint
2 - 2 - يزاﻮﻣ تﺎﺑر ﻲﺳﺪﻨﻫ رﺎﺘﺧﺎﺳ RUR2
R - 4
ﻲﻜﻴﺗﺎﻤﻨﻴﺳ هﺮﻴﺠﻧز ﻲﻠﻛ حﺮﻃ يزاﻮﻣ تﺎﺑر زا ماi
RUR2
R - 4
ﻞﻜﺷ رد 5
ﺖﺳا هﺪﺷ هدروآ .
تﺎﺑر زا ﻲﺻﺎﺧ ﺖﻟﺎﺣ تﺎﺑر ﻦﻳا
يزاﻮﻣ 4 R R R R R− ′′ ′ ′ ′′ ′′
ﻲﻣ ﺪﺷﺎﺑ ﻪﻛ ﺰﺘﻨﺳ نآ ﻊﺟﺮﻣ رد 11]
[
ﺖﺳا هﺪﺷ هدروآ .
نﺎﻤﻫ ﻞﻜﺷ رد ﻪﻛ ﻪﻧﻮﮔ 5
ﻲﻣ ﻪﻈﺣﻼﻣ ،ددﺮﮔ
رﻮﺤﻣ يزاﻮﻣ ﻲﻧارود رﻮﺤﻣ ﺎﺑ ﻲﻳﻻﻮﻟ زاﺪﻧارﺎﻛ ﻚﻳ )z
ﻪﺑ ﻞﺼﺘﻣ
ﺖﺑﺎﺛ يﻮﻜﺳ (
ﻲﻣ ﻞﻴﻜﺸﺗ ار هﺮﻴﺠﻧز ﺮﻫ يدورو ﺪﻫد
. نآ زا ﺲﭘ
نآ ﻲﻧارود رﻮﺤﻣ ﻪﻛ ﺪﻧراد راﺮﻗ ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ ود ﺎﻫ
رد هراﻮﻤﻫ
رﻮﺤﻣ يﺎﺘﺳار ﻲﻣ z
ﺪﺷﺎﺑ . هﺮﻴﺠﻧز ﺮﻫ رد ﻲﻳﺎﻬﺘﻧا ﻞﺼﻔﻣ ود
ﻪﺤﻔﺻ رد هراﻮﻤﻫ ﺰﻴﻧ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ
ﻪﺤﻔﺻ يزاﻮﻣ ﺪﻧراد راﺮﻗ x-y
.
ﺰﻴﻧ تﺎﺑر ﻦﻳا رد د يﺎﻫرﻮﺤﻣ ،
و مﻮﺳ ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ ود نارو
مرﺎﻬﭼ ﻲﻣ ﻢﻫ ﺮﺑ دﻮﻤﻋ و ﻊﻃﺎﻘﺘﻣ لﺎﺳرﻮﻴﻧﻮﻳ ﻞﺼﻔﻣ ﻚﻳ و ﺪﻨﺷﺎﺑ
ﻲﻣ دﺎﺠﻳا ار ﺪﻨﻨﻛ
. نﺎﻳﺎﺷ ﻪﻛ ﺖﺳا ﺮﻛذ 4
ﻞﺼﺘﻣ ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ
يزاﻮﻣ تﺎﺑر رد ﺖﺑﺎﺛ يﻮﻜﺳ ﻪﺑ RUR2
R - ﻤﻫ 4 ياراد هراﻮ
يزاﻮﻣ يﺎﻫرﻮﺤﻣ )
رﻮﺤﻣ يزاﻮﻣ (z
و ﻞﺼﺘﻣ ﻲﻳﻻﻮﻟ ﻞﺼﻔﻣ رﺎﻬﭼ
ﻤﻫ تﺎﺑر ﻦﻳا رد ﻲﻳﺎﻬﻧ ﺮﮕﻠﻤﻋ ﻪﺑ يزاﻮﻣ ﻲﻳﺎﻫرﻮﺤﻣ ياراد هراﻮ
ﻪﺤﻔﺻ ﻲﻣx-y ﺪﻨﺷﺎﺑ .
ﻞﻜﺷ ﻲﻜﻴﺗﺎﻤﻨﻴﺳ هﺮﻴﺠﻧز ﻲﻠﻛ حﺮﻃ5 يزاﻮﻣ تﺎﺑر زا ماi
RUR2
R - 4
ﻲﻣ ﻪﻈﺣﻼﻣ ﺖﻟﺎﺣ ﻪﻛ ددﺮﮔ
مﺰﻴﻧﺎﻜﻣ صﺎﺧ يﺎﻫ يﺎﻫ
يزاﻮﻣ
4 R R R R R− ′′ ′ ′ ′′ ′′
و 4 R R R R R− ′′ ′′ ′′ ′ ′ مﺎﻧ ﺎﺑ
RUR R - 4
هﺪﻳدﺮﮔ ﻲﻓﺮﻌﻣ ﺪﻧا
. نﺎﻤﻫ ﺎﻣا ﻞﻜﺷ رد ﻪﻛ ﻪﻧﻮﮔ يﺎﻫ
1 و 2 ﺰﻴﻧ
ﻲﻣ هﺪﻫﺎﺸﻣ ﺮﺑ ﻢﻛﺎﺣ دﻮﻴﻗ و ﻲﻳﻻﻮﻟ ﻞﺻﺎﻔﻣ يﺎﺘﺳار ،دﻮﺷ
هﺮﻴﺠﻧز ﻦﻳا ﻲﻜﻴﺗﺎﻤﻨﻴﺳ يﺎﻫ
ًﻼﻣﺎﻛ ﺮﮕﻳﺪﻜﻳ ﺎﺑ يزاﻮﻣ تﺎﺑر ود
ﻪﺑﺎﺸﻣ و هدﻮﺑ توﺎﻔﺘﻣ تﺎﺑر ود ﻦﻳا مﺎﻧ ندﻮﺑ
نﺎﺴﻜﻳ ﺮﺑ ﻞﻴﻟد
Bi
θi
Ei
p Di
L1
O
x ri
y z
y′ x′
z′
d′i
Ci
a L2
p
Bi
Ci
Di
Ei
θi L1
L2
O x
ri
y z y′ x′
z′
a d′i
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