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CN112659099B - Local two-degree-of-freedom rigid-flexible coupling bionic robot waist joint - Google Patents

Local two-degree-of-freedom rigid-flexible coupling bionic robot waist joint Download PDF

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CN112659099B
CN112659099B CN202011289393.4A CN202011289393A CN112659099B CN 112659099 B CN112659099 B CN 112659099B CN 202011289393 A CN202011289393 A CN 202011289393A CN 112659099 B CN112659099 B CN 112659099B
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CN112659099A (en
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周玉林
祁柏
褚宏鹏
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Yanshan University
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Abstract

The invention discloses a local two-degree-of-freedom rigid-flexible coupling bionic robot waist joint which comprises four parallel units, wherein the four parallel units are overlapped from bottom to top and respectively comprise a first parallel unit, a second parallel unit, a third parallel unit and a fourth parallel unit from bottom to top, the first parallel mechanism unit and the fourth parallel mechanism unit have the same structure, and the second parallel mechanism unit and the third parallel mechanism unit have the same structure; a flexible shared platform is arranged between every two adjacent parallel units of the four parallel units, a flexible fixed platform is arranged at the bottom end of the first parallel unit, a flexible movable platform is arranged at the top end of the fourth parallel unit, a rigid central branch, a flexible constraint branch and artificial muscles are arranged between the two adjacent platforms, the artificial muscles are uniformly distributed along the circumferential direction, and the head end and the tail end of each artificial muscle are vertically hinged with the two adjacent platforms respectively; the invention has high simulation and good application market prospect.

Description

一种局部二自由度刚柔软耦合仿生机器人腰关节A local two-degree-of-freedom rigid-soft coupled bionic robot waist joint

技术领域technical field

本发明涉及一种仿人机器人技术领域,尤其是一种局部二自由度刚柔软耦合仿生机器人腰关节。The invention relates to the technical field of a humanoid robot, in particular to a waist joint of a local two-degree-of-freedom rigid-soft coupling bionic robot.

背景技术Background technique

人体的腰关节主要作用是连接下肢与躯干,其功能不单是提供转动自由度,还能感受躯干与下肢之间的力。对于仿生机器人来说,采用串联机构虽然有较大的工作空间,但其往往存在累计误差高、负载能力差等问题,因此并联机构成为了腰关节仿生的首选。经过对现有相关技术文献检索发现,发明专利CN101695838A中提出了一种三转一移的并联机构,相比其他串联机构的确降低了累计误差、提高了负载能力;发明专利CN108393872A中提出了一中并联单元耦联机构,增加了机构灵活性以及工作空间。但上述机器人关节均为刚性关节,与刚柔软耦合、运动感知一体的人体腰关节在结构和性能上还有一定的差距。The main function of the waist joint of the human body is to connect the lower limbs with the trunk. Its function is not only to provide rotational freedom, but also to feel the force between the trunk and the lower limbs. For bionic robots, although the series mechanism has a large working space, it often has problems such as high cumulative error and poor load capacity. Therefore, the parallel mechanism has become the first choice for waist joint bionics. After searching the existing related technical documents, it is found that a parallel mechanism with three transfers and one shift is proposed in the invention patent CN101695838A, which reduces the cumulative error and improves the load capacity compared with other series mechanisms; the invention patent CN108393872A proposes a parallel mechanism The parallel unit coupling mechanism increases the flexibility of the mechanism and the working space. However, the above-mentioned robot joints are all rigid joints, and there is still a certain gap in the structure and performance of the human waist joint with rigid-soft coupling and motion perception.

发明内容SUMMARY OF THE INVENTION

本发明是提供一种局部二自由度刚柔软耦合仿生机器人腰关节,解决了现有仿生机器人腰关节柔性差,不具备力感知能力的缺点。The invention provides a waist joint of a local two-degree-of-freedom rigid-soft coupled bionic robot, which solves the shortcomings of the existing bionic robot's poor flexibility and lack of force perception capability.

为解决上述技术问题,本发明所采用的技术方案是:For solving the above-mentioned technical problems, the technical scheme adopted in the present invention is:

一种局部二自由度刚柔软耦合仿生机器人腰关节,包括四个并联单元由下至上叠加而成,其特征在于:所述四个并联单元由下至上分别为第一并联单元、第二并联单元、第三并联单元、第四并联单元,第一并联机构单元与第四并联机构单元结构相同,所述第二并联机构单元与第三并联机构单元结构相同;所述四个并联单元每相邻两个之间设置柔性共用平台,所述第一并联单元底端设置柔性定平台,所述第四并联单元顶端设置柔性动平台,相邻两个平台之间包括刚性中心分支、柔性约束分支、人造肌肉,所述人造肌肉沿周向均匀分布,人造肌肉首尾两端分别与相邻的两个平台垂直铰接。A local two-degree-of-freedom rigid-soft coupled bionic robot waist joint, comprising four parallel units superimposed from bottom to top, characterized in that: the four parallel units are respectively a first parallel unit and a second parallel unit from bottom to top , the third parallel unit, the fourth parallel unit, the first parallel mechanism unit has the same structure as the fourth parallel mechanism unit, the second parallel mechanism unit has the same structure as the third parallel mechanism unit; the four parallel units are adjacent to each other. A flexible shared platform is arranged between the two, a flexible fixed platform is arranged at the bottom of the first parallel unit, a flexible moving platform is arranged at the top of the fourth parallel unit, and a rigid center branch, a flexible constraint branch, The artificial muscle is evenly distributed along the circumferential direction, and both ends of the artificial muscle are vertically hinged with two adjacent platforms respectively.

本发明技术方案的进一步改进在于:所述柔性定平台包括三条力感应分支a,所述三条力感应分支a一端通过柔性铰链相互连接,三条力感应分支a相互间隔120°状,另一端通过铰链连接转接平台,所述力感应分支a内部设置应变片,所述柔性动平台与柔性定平台结构相同。A further improvement of the technical solution of the present invention is that: the flexible fixed platform includes three force-sensing branches a, one end of the three force-sensing branches a is connected to each other by a flexible hinge, the three force-sensing branches a are spaced 120° from each other, and the other end is connected by a hinge Connect the transfer platform, the force sensing branch a is provided with a strain gauge inside, and the flexible moving platform has the same structure as the flexible fixed platform.

本发明技术方案的进一步改进在于:所述柔性共用平台包括分为设置在第一并联单元和第二并联单元之间的柔性共用平台a,设置在第二并联单元和第三并联单元之间的柔性共用台b,以及设置在第三并联单元和第四并联单元之间的柔性共用平台c。A further improvement of the technical solution of the present invention is that the flexible shared platform includes a flexible shared platform a arranged between the first parallel unit and the second parallel unit, and a flexible shared platform a arranged between the second parallel unit and the third parallel unit. A flexible shared platform b, and a flexible shared platform c disposed between the third parallel unit and the fourth parallel unit.

本发明技术方案的进一步改进在于:所述柔性共用平台a包括六条相同的力感应分支b,每两条力感应分支b一端通过柔性铰链相互连接;每三条力感应分支b另一端通过铰链相互连接,六条力感应分支b构成纺锤体状,所述柔性共用平台a上下两端之间设置弹簧进行缓冲。A further improvement of the technical solution of the present invention is that: the flexible shared platform a includes six identical force-sensing branches b, one end of every two force-sensing branches b is connected to each other through a flexible hinge; the other end of every three force-sensing branches b is connected to each other through a hinge , the six force-sensing branches b form a spindle shape, and springs are arranged between the upper and lower ends of the flexible shared platform a for buffering.

本发明技术方案的进一步改进在于:所述柔性定平台和柔性共用平台a之间设置刚性中心分支a、柔性约束分支a和人造肌肉a,柔性共用平台a和柔性共用平台b之间设置刚性中心分支b、柔性约束分支b和人造肌肉b,柔性共用平台b和柔性共用平台c之间设置刚性中心分支c、柔性约束分支c和人造肌肉c,柔性共用平台c和柔性动平台之间设置刚性中心分支d、柔性约束分支d和人造肌肉d。A further improvement of the technical solution of the present invention is that a rigid center branch a, a flexible restraint branch a and an artificial muscle a are arranged between the flexible fixed platform and the flexible shared platform a, and a rigid center is arranged between the flexible shared platform a and the flexible shared platform b Branch b, flexible restraint branch b and artificial muscle b, rigid central branch c, flexible restraint branch c and artificial muscle c are set between flexible shared platform b and flexible shared platform c, and rigid central branch c is set between flexible shared platform c and flexible moving platform The central branch d, the flexible restraint branch d, and the artificial muscle d.

本发明技术方案的进一步改进在于:所述刚性中心分支a包括第一虎克铰链、第二虎克铰链和第五连杆,所述第一虎克铰链、第二虎克铰链分别与第五连杆上下串联,所述柔性约束分支a包括两个连杆分别为第一连杆、第二连杆,所述第一连杆一端通过第一转动副与柔性定平台连接,另一端与第二连杆通过第二转动副连接,所述第二连杆另一端通过第三转动副连接柔性共用平台a,所述刚性中心分支b、刚性中心分支c、刚性中心分支d结构均与刚性中心分支a相同,所述柔性约束分支b、柔性约束分支c、柔性约束分支d结构均与柔性约束分支a结构相同。A further improvement of the technical solution of the present invention is that the rigid central branch a includes a first Hooker hinge, a second Hooker hinge and a fifth connecting rod, and the first Hooker hinge and the second Hooker hinge are respectively connected to the fifth connecting rod. The connecting rods are connected in series up and down, the flexible restraint branch a includes two connecting rods, namely a first connecting rod and a second connecting rod, one end of the first connecting rod is connected with the flexible fixed platform through a first rotating pair, and the other end is connected with the first connecting rod The two links are connected by a second rotation pair, and the other end of the second link is connected to the flexible shared platform a through a third rotation pair. The rigid center branch b, the rigid center branch c, and the rigid center branch d are all connected to the rigid center The branch a is the same, and the structures of the flexible restraint branch b, the flexible restraint branch c, and the flexible restraint branch d are all the same as the structure of the flexible restraint branch a.

由于采用了上述技术方案,本发明取得的技术进步是:Owing to having adopted the above-mentioned technical scheme, the technical progress that the present invention obtains is:

仿生腰关节由柔性平台构成,集运动、力感知功能于一体,四个局部二自由度并联单元组合成八自由度关节,增加机构灵活性可实现较复杂的仿真行为,替代传统的简单结构的机械腰关节,仿生机器人腰关节由刚性分支、柔性分支和软体驱动构成使得具有较高的拟真性,具有较好的市场应用前景。The bionic waist joint is composed of a flexible platform, which integrates motion and force sensing functions. Four local two-degree-of-freedom parallel units are combined into an eight-degree-of-freedom joint. Increasing the flexibility of the mechanism can realize more complex simulation behaviors and replace the traditional simple structure. Mechanical waist joints, bionic robot waist joints are composed of rigid branches, flexible branches and software drives, which make them have high fidelity and have good market application prospects.

附图说明Description of drawings

图1为整体结构立体示意图;Fig. 1 is a three-dimensional schematic diagram of the overall structure;

图2为第一并联单元立体示意图;2 is a schematic perspective view of a first parallel unit;

图3为第一并联单元偏转立体示意图;3 is a schematic perspective view of the deflection of the first parallel unit;

图4为第二并联单元立体示意图;4 is a schematic perspective view of a second parallel unit;

图5为柔性定平台立体示意图;5 is a three-dimensional schematic diagram of a flexible fixed platform;

图6为柔性共用平台立体示意图;6 is a three-dimensional schematic diagram of a flexible shared platform;

图7为刚性中心分支立体示意图;FIG. 7 is a schematic perspective view of a rigid center branch;

其中,010、柔性定平台,011、力感应分支a,012、应变片,013、转接平台,014、柔性铰链,020、柔性共用平台a,021、力感应分支b,022、应变片,023、弹簧,024、柔性铰链,030、柔性共用平台b,040、柔性共平台c,050、柔性动平台,060、柔性约束分支a,061、第一转动副,062、第一连杆,063、第二转动副,064、第二连杆,065、第三转动副,070、柔性约束分支b,080、柔性约束分支c,090、柔性约束分支d,100、刚性中心分支a,101、第一虎克铰链,102、第五连杆,103、第二虎克铰链,110、刚性中心分支b,120、刚性中心分支c,130、刚性中心分支d,140、人造肌肉a,150、人造肌肉b,160、人造肌肉c,170、人造肌肉d。Among them, 010, flexible fixed platform, 011, force sensing branch a, 012, strain gauge, 013, transfer platform, 014, flexible hinge, 020, flexible shared platform a, 021, force sensing branch b, 022, strain gauge, 023, spring, 024, flexible hinge, 030, flexible shared platform b, 040, flexible shared platform c, 050, flexible moving platform, 060, flexible constraint branch a, 061, first rotation pair, 062, first link, 063, the second rotation pair, 064, the second link, 065, the third rotation pair, 070, the flexible restraint branch b, 080, the flexible restraint branch c, 090, the flexible restraint branch d, 100, the rigid center branch a, 101 , the first hook hinge, 102, the fifth link, 103, the second hook hinge, 110, the rigid central branch b, 120, the rigid central branch c, 130, the rigid central branch d, 140, the artificial muscle a, 150 , artificial muscle b, 160, artificial muscle c, 170, artificial muscle d.

具体实施方式Detailed ways

一种局部二自由度刚柔软耦合仿生机器人腰关节,包括四个并联单元由下至上叠加而成,四个并联单元由下至上分别为第一并联单元、第二并联单元、第三并联单元、第四并联单元,第一并联机构单元与第四并联机构单元结构相同,第二并联机构单元与第三并联机构单元结构相同;四个并联单元每相邻两个之间设置柔性共用平台,分别为柔性共用平台a、柔性共用平台b、柔性共用平台c,所述第一并联单元底端设置柔性定平台010,柔性定平台010包括三条力感应分支a,所述三条力感应分支a一端通过柔性铰链相互连接,三条力感应分支a相互间隔120°状,另一端通过铰链连接转接平台,所述力感应分支a内部设置应变片012,应变片012用于测量感应分支上的受力,所述柔性动平台与柔性定平台结构相同;第四并联单元顶端设置结构与柔性定平台010相同的柔性动平台050,柔性定平台010和柔性共用平台a之间设置刚性中心分支a、柔性约束分支a和人造肌肉a,柔性共用平台a和柔性共用平台b之间设置刚性中性分支b、柔性约束分支b和人造肌肉b,柔性共用平台b和柔性共用平台c040之间设置刚性中心分支c、柔性约束分支c和人造肌肉c,柔性共用平台c和柔性动平台d之间设置刚性中心分支d、柔性约束分支d和人造肌肉d,相邻两个平台之间通过刚性中心分支、柔性约束分支、人造肌肉连接形成局部两自由度并联关节,整个刚柔软耦合仿生机器人腰关节为八自由度关节,其中刚性中心分支a包括第一虎克铰链101、第二虎克铰链103和第五连杆102,所述第一虎克铰链101、第二虎克铰链103分别与第五连杆102上下串联,柔性约束分支a包括两个连杆分别为第一连杆062、第二连杆064,所述第一连杆062一端通过第一转动副061与柔性定平台010连接,另一端与第二连杆064通过第二转动副063连接,所述第二连杆064另一端通过第三转动副065连接柔性共用平台a,刚性中心分支b、刚性中心分支c、刚性中心分支d结构均与刚性中心分支a相同。A local two-degree-of-freedom rigid-soft coupled bionic robot waist joint, comprising four parallel units superimposed from bottom to top, the four parallel units from bottom to top are a first parallel unit, a second parallel unit, a third parallel unit, The fourth parallel unit, the first parallel mechanism unit has the same structure as the fourth parallel mechanism unit, and the second parallel mechanism unit has the same structure as the third parallel mechanism unit; a flexible shared platform is arranged between each adjacent two of the four parallel units, respectively. It is a flexible shared platform a, a flexible shared platform b, and a flexible shared platform c. The bottom end of the first parallel unit is provided with a flexible fixed platform 010. The flexible fixed platform 010 includes three force-sensing branches a, and one end of the three force-sensing branches a passes through. The flexible hinges are connected to each other, the three force-sensing branches a are spaced 120° apart from each other, and the other end is connected to the transfer platform through hinges. The force-sensing branch a is internally provided with a strain gauge 012, and the strain gauge 012 is used to measure the force on the sensing branch, The flexible moving platform has the same structure as the flexible fixed platform; the top of the fourth parallel unit is provided with a flexible moving platform 050 with the same structure as the flexible fixed platform 010, and a rigid central branch a and a flexible constraint are arranged between the flexible fixed platform 010 and the flexible shared platform a. A rigid neutral branch b, a flexible constraint branch b and an artificial muscle b are set between the branch a and the artificial muscle a, the flexible shared platform a and the flexible shared platform b, and the rigid central branch c is set between the flexible shared platform b and the flexible shared platform c040 , a flexible constraint branch c and an artificial muscle c, a rigid central branch d, a flexible constraint branch d and an artificial muscle d are set between the flexible shared platform c and the flexible moving platform d, and the rigid central branch and flexible constraint are arranged between two adjacent platforms. The branches and artificial muscles are connected to form a local two-degree-of-freedom parallel joint, and the entire rigid-soft coupled bionic robot waist joint is an eight-degree-of-freedom joint, wherein the rigid center branch a includes the first Hooker hinge 101, the second Hooker hinge 103 and the fifth joint. The rod 102, the first Hook hinge 101 and the second Hook hinge 103 are connected in series with the fifth connecting rod 102 up and down respectively, and the flexible restraint branch a includes two connecting rods, namely the first connecting rod 062 and the second connecting rod 064 , one end of the first link 062 is connected with the flexible fixed platform 010 through the first rotating pair 061, the other end is connected with the second link 064 through the second rotating pair 063, and the other end of the second link 064 is connected through the third The rotating pair 065 is connected to the flexible shared platform a, and the rigid central branch b, the rigid central branch c, and the rigid central branch d have the same structure as the rigid central branch a.

其中,柔性共用平台包括分为设置在第一并联单元和第二并联单元之间的柔性共用平台a,设置在第二并联单元和第三并联单元之间的柔性共用台b,以及设置在第三并联单元和第四并联单元之间的柔性共用平台c,三个柔性共用平台结构相同,具体的柔性共用平台a包括六条相同的力感应分支b,每两条力感应分支b一端通过柔性铰链相互连接;每三条力感应分支b另一端通过铰链相互连接,六条力感应分支b构成纺锤体状,所述柔性共用平台a上下两端之间设置弹簧进行缓冲。The flexible sharing platform includes a flexible sharing platform a arranged between the first parallel unit and the second parallel unit, a flexible sharing platform b arranged between the second parallel unit and the third parallel unit, and a flexible sharing platform b arranged between the second parallel unit and the third parallel unit. The flexible shared platform c between the three parallel units and the fourth parallel unit, the three flexible shared platforms have the same structure, the specific flexible shared platform a includes six identical force-sensing branches b, and one end of each two force-sensing branches b passes through a flexible hinge Connected to each other; the other ends of every three force-sensing branches b are connected to each other by hinges, and the six force-sensing branches b form a spindle shape, and springs are provided between the upper and lower ends of the flexible shared platform a for buffering.

仿生机器人腰关节的四个并联单元的内部机构大致相同,第一并联机构单元中,柔性定平台010与相邻的柔性共用平台a通过三条柔性约束分支a、刚性中心分支a、三组人造肌肉a连接。柔性约束分支060通过第一连杆062、第二连杆064,所述第一连杆062一端通过第一转动副061与柔性定平台010连接,另一端与第二连杆064通过第二转动副063连接,所述第二连杆064另一端通过第三转动副065连接柔性共用平台a,刚性中心分支a上的第五连杆102与柔性定平台010通过第一虎克铰链101连接,与柔性共用平台a通过第二虎克铰链103连接;人造肌肉a一端与柔性定平台010铰接,另一端与柔性共用平台a铰接,柔性约束分支b、柔性约束分支c、柔性约束分支d结构均与柔性约束分支a结构相同。The internal mechanisms of the four parallel units of the bionic robot waist joint are roughly the same. In the first parallel mechanism unit, the flexible fixed platform 010 and the adjacent flexible shared platform a pass through three flexible constraint branches a, rigid central branch a, and three sets of artificial muscles. a connection. The flexible restraint branch 060 passes through a first link 062 and a second link 064. One end of the first link 062 is connected to the flexible fixed platform 010 through a first rotation pair 061, and the other end is connected to the second link 064 through a second rotation. The pair 063 is connected, the other end of the second link 064 is connected to the flexible shared platform a through the third rotating pair 065, the fifth link 102 on the rigid central branch a is connected to the flexible fixed platform 010 through the first Hooke hinge 101, It is connected with the flexible shared platform a through the second Hooke hinge 103; one end of the artificial muscle a is hinged with the flexible fixed platform 010, and the other end is hinged with the flexible shared platform a. The structures of the flexible restraint branch b, the flexible restraint branch c, and the flexible restraint branch d are all It has the same structure as the flexible constraint branch a.

Claims (5)

1. The utility model provides a just soft coupling bionic robot waist joint of local two degrees of freedom, includes that four parallel unit are formed by supreme stack from bottom to top, its characterized in that: the four parallel units are respectively a first parallel unit, a second parallel unit, a third parallel unit and a fourth parallel unit from bottom to top, the first parallel mechanism unit and the fourth parallel mechanism unit have the same structure, and the second parallel mechanism unit and the third parallel mechanism unit have the same structure; a flexible shared platform is arranged between every two adjacent four parallel units, a flexible fixed platform (010) is arranged at the bottom end of the first parallel unit, a flexible movable platform (050) is arranged at the top end of the fourth parallel unit, a rigid central branch, a flexible constraint branch and artificial muscles are arranged between every two adjacent platforms, the artificial muscles are uniformly distributed along the circumferential direction, and the head end and the tail end of each artificial muscle are vertically hinged with the two adjacent platforms respectively; the flexible shared platform comprises a flexible shared platform a (020) arranged between the first parallel unit and the second parallel unit, a flexible shared platform b (030) arranged between the second parallel unit and the third parallel unit, and a flexible shared platform c (040) arranged between the third parallel unit and the fourth parallel unit; the flexible shared platform a (020) comprises six identical force sensing branches b (021), and one end of each two force sensing branches b (021) is connected with each other through a flexible hinge (024); the other ends of every three force induction branches b (021) are mutually connected through a hinge; the rigid central branch comprises a rigid central branch a (100), a rigid central branch c (120) and a rigid central branch d (130), the rigid central branch a (100) comprises a first Hooke hinge (101), a second Hooke hinge (103) and a fifth connecting rod (102), the first Hooke hinge (101) and the second Hooke hinge (103) are respectively connected with the fifth connecting rod (102) in series up and down, and the structures of the rigid central branch b (110), the rigid central branch c (120) and the rigid central branch d (130) are the same as those of the rigid central branch a (100).
2. The waist joint of the local two-degree-of-freedom rigid-flexible coupling bionic robot as claimed in claim 1, wherein: the flexible fixed platform (010) comprises three force sensing branches a (011), one ends of the three force sensing branches a (011) are connected with each other through a flexible hinge (014), the three force sensing branches a (011) are separated by 120 degrees, the other ends of the three force sensing branches are connected with a switching platform (013) through hinges, a strain gauge (012) is arranged inside the force sensing branches a (011), and the flexible movable platform (050) is identical to the flexible fixed platform (010) in structure.
3. The local two-degree-of-freedom rigid-soft coupling bionic robot waist joint as claimed in claim 1, wherein: six force sensing branches b (021) form a spindle shape, and a spring (023) is arranged between the upper end and the lower end of the flexible shared platform a (020) for buffering.
4. The local two-degree-of-freedom rigid-soft coupling bionic robot waist joint as claimed in claim 1, wherein: a rigid central branch a (100), a flexible constraint branch a (060) and an artificial muscle a (140) are arranged between the flexible fixed platform (010) and the flexible shared platform a (020), a rigid central branch b (110), a flexible constraint branch b (070) and an artificial muscle b (150) are arranged between the flexible shared platform a (020) and the flexible shared platform b (030), a rigid central branch c (120), a flexible constraint branch c (080) and an artificial muscle c (160) are arranged between the flexible shared platform b (030) and the flexible shared platform c (040), and a rigid central branch d (130), a flexible constraint branch d (090) and an artificial muscle d (170) are arranged between the flexible shared platform c (040) and the flexible movable platform (050).
5. The local two-degree-of-freedom rigid-flexible coupling bionic robot waist joint as claimed in claim 4, characterized in that: the flexible constraint branch a (060) comprises two connecting rods, namely a first connecting rod (062) and a second connecting rod (064), one end of the first connecting rod (062) is connected with the flexible fixed platform (010) through a first revolute pair (061), the other end of the first connecting rod is connected with the second connecting rod (064) through a second revolute pair (063), the other end of the second connecting rod (064) is connected with the flexible shared platform a through a third revolute pair (065), and the structures of the flexible constraint branch b (070), the flexible constraint branch c (080) and the flexible constraint branch d (090) are the same as the structure of the flexible constraint branch a (060).
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