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Research ArticleKinematic Decoupling Analysis and Design of a BiomimeticRobotic Elbow Joint

Bingyan Cui 123 Liwen Chen 1 Yongtao Xie 1 and Zhijun Wang1

1College of Mechanical Engineering North China University of Science and Technology Tangshan 063009 China2Yanshan University Qinhuangdao 066009 China3Widex Sanitary Co Ltd Tangshan 063000 China

Correspondence should be addressed to Bingyan Cui mj_cby126com

Received 27 November 2017 Revised 30 March 2018 Accepted 15 April 2018 Published 9 May 2018

Academic Editor Liwei Shi

Copyright copy 2018 Bingyan Cui et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The research of a biomimetic robotic manipulator is based on the flexible characteristics of the human upper limb joint and abiomimetic robotic elbow joint plays a very significant role in the kinematic control of the biomimetic robotic manipulatorMost robotic elbow joints encountered today have a common disadvantage of bad neutrality low rotational capability and poorbiomimetics To overcome some difficulties this paper presents a novel biomimetic robotic elbow joint The structural model ofthe elbow joint is described and the position equation is solved Secondly the kinematic equation of the elbow joint isestablished the kinematic decoupling performance evaluation index of the elbow joint is defined the kinematic decouplingcharacteristics of the elbow joint are analyzed and the kinematic decoupling performance map in the workspace is drawnThirdly using the spatial model theory the structural parameters of the elbow joint are optimized the structural parameters areselected by the Monte Carlo method and the novel biomimetic robotic elbow joint is designed The analysis results showing thekinematic decoupling performance of the elbow joint are symmetrical and the kinematic decoupling performance decreases withthe increase of the angle and there is a good kinematic decoupling in the workspace of about 35 in the vicinity of the initialposition When the structural parameters of the elbow joint are Re1 = 90mm Re2 = 70mm and Re3 = 30mm the elbow joint hasa very good kinematic decoupling This paper can lay a foundation for further analysis and research of the biomimetic roboticelbow joint

1 Introduction

Biomimetic robotics is a new branch in the field of robotresearches which have integrated the biomimetic principleinto the design and control of the robot and could imitatestructure and movement characteristics of animals orhumans The motion behavior and some functions of naturalorganism have provided a great deal of thinking sources forrobot scientists to design and realize flexible control [1ndash3]With flexible operation and movement features biomimeticrobotics based on various types of bionic joints hashighlighted good application prospects in the fields of rehabil-itation medicine space exploration rescue and so on [4ndash6]

The research of a biomimetic robotic manipulator isbased on the flexible characteristics of the human upper limb

joint and dexterous hands and the human upper limbs arecomposed of the shoulder joint elbow joint wrist joint andfinger joint to complete the complex work and reflect theflexibility of the whole limb movement The more flexiblethe upper limb joint the more flexible the upper limbmovement can be controlled [7] Li et al [8] designed anovel 3-DOF shoulder joint established the error perfor-mance index and plotted the error map Li et al [9] proposeda bionic eye based on a 3-DOF spherical parallel mechanismand the structure parameters of the bionic eye were opti-mized Klein et al [10] designed a 3-DOF exoskeleton shoul-der joint and the torque capacity character curve is obtainedZhang and Jin [11] made an in-depth study of theory on thedriving characteristics obtained dynamic characteristics andoptimized size of a 3-DOF shoulder joint Sun et al [12]

HindawiApplied Bionics and BiomechanicsVolume 2018 Article ID 4613230 9 pageshttpsdoiorg10115520184613230

proposed a wrist joint based on a spherical 3-DOF paralleldecoupling mechanism and the position of the wrist jointwas analyzed

Cui and Jin [13] presented a 2-DOF elbow joint definedthe static performance index and obtained the static perfor-mance curve In 2015 a novel hip joint is designed and itsdynamic characters and structural parameters have studied[14] Xu et al [15] designed an elbow joint based on largedeceleration ratio traction motor direct drive structure andanalyzed the force character and the elbow provided effectiveflexion and extension movement based on the double-screw-pair transmission and the elbow joint developed and com-pleted flexion and extension movement [16] Hwang et al[17] proposed a novel elbow based on a slider-crank mecha-nism and obtained the force transmission property curveStanišić and Goehler [18] proposed a hybrid shoulder mech-anism for copying the grasping movement and a mechanismcapable of reproducing voluntary human reaching motions isintroduced along with the procedural method of implement-ing the coupled motions Lovasz et al [19] designed an elbowmodule carried on remote control for a haptic arm exoskel-eton and proposed several design solutions and a controlstrategy A biomimetic robotic elbow joint plays a very signif-icant role in the motion control of a biomimetic roboticmanipulator The kinematic decoupling is an importantindex which affects the overall motion and the control ofthe biomimetic robotic elbow joint The kinematic decou-pling of the mechanism [20] can determine its kinematiccharacteristics and provide the basis for the robot controland trajectory planning

The problem of decoupling is closely related to theJacobian matrix of the biomimetic robotic joint Researchershave studied less in this field Gong et al [21] proposed thedecoupling of the moving coordinates in the absolute coordi-nates and verified the decoupling theory by the correspond-ing examples Shen et al [22] analyzed the kinematicdecoupling of a 6-DOF parallel mechanism Xu et al [23]studied the 2R1T parallel mechanism on the principle of itsmotion decoupling based on the positional relationshipbetween the actuation force and the rotational axis Essombaand Nguyen Vu [24] presented a novel spherical decoupledmechanism and proved the decoupling motion by itskinematic and velocity models

Based on the analysis of the literature the existing roboticelbow joint is usually able to achieve flexion and extensionThe structure of elbow joint design adopts a series structurethe series structure lacks good centering ability From theanalysis of the performance of elbow joints there are manyliteratures on the bearing capacity of elbow joints and the lit-erature of the kinematic decoupling has not been seen yet Onthis basis this paper proposes a biomimetic robotic elbowjoint The biomimetic robotic elbow joint adopts a 2-DOFspherical parallel mechanism as a prototype which hasadvantages of good structural characteristics large range ofmotion and high bearing capacity and was compared withthe 3-DOF parallel mechanism in the 863 project From theanalysis of the degree of freedom of the mechanism the3-DOF spherical parallelmechanismhas three degrees of free-dom in accordance with the requirements of the prosthetic

prototype of the shoulder joint and the human elbow jointstructure has two degrees of freedom of movement character-istics so the elbow joint mechanism has very good bionicstructure From the analysis of the installation of the mecha-nism the rotation center of the 3-DOF spherical parallelmechanism is located in the middle of the moving platformand the static platform The neutrality requirements for therods during installation are very high and difficult to installThe rotation center of each rod of the biomimetic roboticelbow joint presents 90 degrees which is convenient to installand has good neutrality

In this paper the kinematic equation of the biomi-metic robotic elbow joint is established the Jacobianmatrix is derived the kinematic decoupling performanceevaluation index of the biomimetic robotic elbow joint isdefined the kinematic decoupling performance evaluationindex map is drawn in the workspace and the global kine-matic decoupling performance index is established basedon the kinematic decoupling analysis Based on the spacemodel theory the structural parameters of the elbow jointare optimized and selected by the Monte Carlo methodand the biomimetic robotic elbow joint is designed Thepurpose of the decoupling analysis of the elbow joint isto make the control of the elbow joint mechanism moreconvenient and easier

2 The Model and Position Analysis

21 The Structural Description The biomimetic roboticelbow joint is an important joint of the biomimetic handOn the base of the knowledge of bionics the human elbowjoint is composed of the humerus radius ulna and ligamentThe human elbow joint is limited to the connection betweenthe three bones and the ligament which can only rotateabout two axes and can realize movement of internal rotationand external rotation and flexion and extension as shown inFigure 1

The structure design of the biomimetic robotic elbowjoint should be able to realize the movement of theanthropomorphic elbow joint According to the analysisof joint structure and kinematic characteristics of thehuman elbow joint this paper proposed a novel biomi-metic robotic elbow joint based on a 2-DOF orthogonalspherical parallel mechanism The elbow joint has two

Humerus

UlnaLigament

Radius

Figure 1 Schematic diagram of the human elbow joint

2 Applied Bionics and Biomechanics

moving branches the frame and the moving platformwhich contain two driving motors and the driving motoris fixed on the frame The moving platform of the elbowjoint is connected by the arm connector and connectedwith the ring through the rotating pair The elbow jointcan realize two degrees of freedom of rotation and hasadvantages of good bionic characteristics small structureand little inertial forces The structure diagram is shownin Figure 2

Two Cartesian coordinates the base frame Ce isfixed and represented by the coordinate Xe Y e Ze whilethe moving platform has a frame Ke attached to it withcoordinates ixiyiz The coordinate center of the two coor-dinate systems is coincident and the center point of coor-dinates is Oe The plane Ao is composed of OeAe1 andOeAe4 axes The Xe axis is along OeAe8 the vector direc-tion the Ye axis is along OeAe5 the vector direction andpasses and the Ze axis is vertical to the plane Ao andalong OeAe2 the vector direction ℓ1 is the unit vector ofOeAe2 axes ℓ2 is the unit vector of OeAe5 axes ℓ3 is theunit vector along OeAe3 ℓ4 is the unit vector of OeAe1axes and ℓ5 is the unit vector of OeAe4 axes

Assume that the spherical radius of the reference centerof the connection rotation pairs Ae1 and Ae4 is Re1 thespherical radius of the reference center of the connectionrotation pairs Ae3 and Ae5 is Re2 and the spherical radiusof the reference center of the connection rotation pairs Ae2is Re3 Therefore the reference centers of the rotation pairsare distributed on concentric spherical surfaces with differ-ent radii Re3 lt Re2 lt Re1 Thus the structural parametersof the elbow joint are Re1 Re2 and Re3

22 Derivation of Position Forward Solution The kinematicequation of the elbow joint is established based on the solu-tion of the inverse position The attitude angles of the elbowjoint moving platform are γe and βe and the input angles areγe and βe The moving platform of the elbow joint can rotatearound the X axis and the Y axis and the correspondingtransformation matrix of the elbow joint moving platformis introduced and can be written as

Te = T X γe T Y βe

=

cos βe 0 sin βe

sin γesin βe cos γe minussin γecos βe

minuscos γesin βe sin γe cos γecos βe

1

In the fixed coordinate system the unit vector ℓ2 can beexpressed as

ℓ2 = Te

010

=0

cos γesin γe

2

According to the mechanism characteristics of theelbow joint the input angle of the drive motor is εe1 and theunit vector ℓ2 can be expressed as the input angle εe1 and isgiven by

ℓ2 =1 0 00 cos εe1 minussin εe1

0 sin εe1 cos εe1

010

=0cos εe1sin εe1

3

Comparison of (2) and (3) can be obtained as

εe1 = γe 4


ℓ3 = Te

100

=cos βe

sin γesin βe

minussin γecos βe

5

In the fixed coordinate system the unit vector ℓ1 is repre-sented by the input angle εe2 and is given by

ℓ1 =cos εe2 0 sin εe2

0 1 0minussin εe2 0 cos εe2

001

=sin εe2

0cos εe2

6

According to the geometry of the elbow joint (7) canbe obtained

ℓ1 sdot ℓ3 = 0 7

Equations (2) and (3) can be written in the form of (7)and can be derived as

εe2 = a tan 2 cos γe sin βe cos βe 8

The inverse position solution equation of the elbow jointcan be written as

εe1 = γeεe2 = a tan 2 cos γe sin βe cos βe

9

Ae1

Ae2

Xe

Ye

Ae3

Ae4

Ze

Ae5

Oe

9857474

9857475

9857473

98574719857472

ix

yi

iz

Ae6

Ae7

Ae8minus9857471

minus9857475

minus9857473

1

2

3 64 5

120576e2

120576e1

Figure 2 The structure of the biomimetic robotic elbow joint1mdashframe 2 and 3mdashconnecting rods 4mdashannular member5mdashmoving platform and 6mdasharm connector

3Applied Bionics and Biomechanics

The forward positive solution equation of the elbow jointby (9) is deduced as

γe = εe1βe = a tan 2 sin εe2 cos εe1 cos εe2

10

3 The Kinematic Decoupling Analysis

31 The Derivation of the Kinematic Equation Differentialtreatment (10) the kinematic equation is obtained as

ϕe = Jeεe 11

where ϕe is the output angle velocity and is expressed as

ϕe = γe βeT εe is the input angle velocity and is expressed

as εe = εe1εe1T and Je is the Jacobian matrix and can be

extracted as

Je =1 0

sin εe1sin εe2cos εe2sin2εe2 + cos2εe1 cos2εe2

cos εe1sin2εe2 + cos2εe1 cos2εe2

12

The kinematic decoupling analysis of the elbow jointdepends on the Jacobian matrix Je In order to describe thedecoupling characteristic in more detail the index of kine-matic decoupling performance is defined as

weierpe =ςe max minus ςe min

ςe max 13

where the maximum and minimum singular values of theelbow joint Jacobian matrix are ςe max and ςe min respectively

32 Analysis of Kinematic Decoupling Performance Thedecoupling analysis of the kinematic of the elbow joint is tostudy the correlation or dependence of the output parameterson the input parameters If the Jacobian matrix Je can beturned into a diagonal matrix the elbow joint is kinematicdecoupling The kinematic decoupling of the elbow jointunder different input conditions is analyzed

(1) When the input angular velocity of the Xe axis is εe1the decoupling of the output angular velocity of theelbow joint is analyzed

The elbow joint has an input angular velocity on theXe axis and the input angular velocity on the Ye axisis εe2 and εe2 = 0 rads The Jacobian matrix of theelbow joint can be obtained from (12) and can begiven by

Je =1 00 1

14

From (14) the Jacobian matrix is a diagonalunit matrix and the evaluation index of thekinematic decoupling performance in the workspaceis always zero so the elbow joint is completely

kinematic decoupling and has the highest decouplingperformance

(2) When the input angular velocities of the Xe axis andYe axis are εe1 and εe2 the elbow joint kinematicdecoupling is analyzed

When the elbow joint is driven by two drivingmotors (12) expresses the Jacobian matrix Withthe decoupling definition of the local motion of theshoulder joint there is only one nonzero element inthe first row of (12) so the elbow joint is locally kine-matic decoupling in the whole workspace Accordingto the kinematic decoupling index of (13) the localkinematic decoupling performance graph of theelbow joint is obtained as shown in Figure 3

In Figure 3 the kinematic decoupling index weierpe changeslittle with the increase of the γe angle With the increaseof the βe angle the kinematic decoupling index weierpeincreases gradually its decoupling becomes smallerand the coupling gradually increases The kinematicdecoupling of the elbow joint is locally decoupling inthe γe angle direction with very good kinematicdecoupling in the region of approximately 35 of theinitial position

4 Global Kinematic Decoupling Analysis andStructural Parameter Optimization

The global performance index can better reflect the kine-matic decoupling of the elbow joint in the whole postureworkspace and the spatial model theory [25 26] provides anew idea for the structural parameter optimization of theelbow joint The structural parameters of the elbow jointare optimized by the theory of the space model which madethe performance evaluation index of kinematic decouplingbetter The structure parameters of the elbow joint wereselected by the Monte Carlo method

035030025020015010005

050

minus50 minus50

500 0

e (120596

e)

120573e (deg)120574e (deg)

Figure 3 Index of the kinematic decoupling performance of outputangle velocity when the input velocity has the Xe axis and Ye axis


41 Analysis of the Global Kinematic Decoupling PerformanceBased on the structural description of the biomimetic roboticelbow joint the structural parameters are Re1 Re2 and Re3The spatial model of the structural parameters of the biomi-metic robotic elbow joint is established The structural dimen-sion parameters of the elbow joint are dimensionless and canbe given as

le =Re1 + Re2 + Re3

3 15

The dimensionless structural dimensions of the elbowjoint are expressed respectively as

le1 =Re1le

le2 =Re2le

le3 =Re3le

16

Formula (16) can be obtained as

le1 + le2 + le3 = 3 17

Considering the manufacturing and assembling of thebiomimetic robotic elbow joint the conditions for the struc-tural parameters are satisfied and can be written as

0 le le3 le le2 le 30 le le1 le 3

18

The three dimensionless structure parameters are Carte-sian axes le1 le2 and le3 respectively The geometric spacemodel of the biomimetic robotic elbow joint and the triangleΔPeQeSe can be obtained by using (15) and (18) as shown inFigure 4 In order to facilitate drawing the three-dimensionalmodel is transformed into a two-dimensional model of the

space model The transformation relation of the dimension-less coordinate is generated as

x = 3 + le2 minus le13

y = le3

19

The global performance index is introduced into the spa-tial model and the global kinematic decoupling performanceindex of the biomimetic robotic elbow joint is defined as

ξe =VeweierpedV e

VedVe

20

where ξe is the global kinematic decoupling performanceindex and V e is the workspace of the elbow joint

Using MATLAB software the global kinematic decou-pling performance map of the elbow joint in the plain geo-metric space model is drawn according to (1) (2) (3) (4)(5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)(17) (18) (19) and (20) as shown in Figure 5 In Figure 5according to (16) the three coordinates le1 le2 and le3 reflectthe three structural parameters Re1 Re2 and Re3 respectively

From Figure 5 the global kinematic decoupling perfor-mance of the elbow joint is linearly distributed With theincrease of Re3 and Re2 the global kinematic decoupling per-formance index values increase and the global kinematic

0

3

3

3le1

le3

le2

Pe

Qe

Se

(a) Three-dimensional model of the spatial

model

3

x

y

3

15

le1

le3

le2

Qe

Se

Pe0

0

0

(b) Two-dimensional model of the spatial model

Figure 4 The spatial model of the biomimetic robotic elbow joint

3x

y

3

15

0

0010

015020

025

005

le1

le3

le2

Se

Pe0 Qe

Figure 5 Globe kinematic decoupling performance evaluationindex atlases of the elbow joint


decoupling decreases gradually With the increase of Re1 theglobal kinematic decoupling performance index valuesdecrease and the global kinematic decoupling increases

42 The Structural Parameter Optimization Structuralparameters have a direct influence on the kinematic perfor-mance of the robot Stan et al [27] defined the optimal func-tion based on stiffness and transmission quality In thispaper the range of structural parameters of the elbow jointis defined For the optimal design of the elbow joint reason-able structural parameters should be selected for design andmanufacturing The analysis of global kinematic decouplingperformance of the elbow joint based on the spatial modeltheory has laid the theoretical foundation for the selectionof the elbow joint structural parameters In this paper basedon the Monte Carlo method the structural parameters of theelbow joint are optimized The reasonable structural param-eters of the elbow joint are obtained by using the probabilitystatistic method

The value range of the global kinematic decoupling per-formance index of the elbow joint is the interval [0 1] whichconforms to the rule of rectangle distribution Combinedwith the structural features of the elbow joint the structuralparameter ranges of the elbow joint Re1 Re2 and Re3 areRe1 isin 60 90 mm Re2 isin 40 70 mm and Re3 isin 20 50 mm

In [28] the structural parameters of the mechanicalarm are optimized using the Monte Carlo method andthe intermediate value of the performance index is selectedas the structural parameter optimization objective There-fore the intermedia value of the global kinematic decou-pling index of the elbow joint is used as the optimaltarget of the elbow joint in which ξe = 0 1524 When ξeis not more than 01524 the global kinematic decouplingperformance is better

Under the condition that the evaluation index of theglobal kinematic decoupling performance is better than theoptimization target value the distribution rule of samplingvalues of each parameter counted the sampling within therange of structural parameters and the probability distribu-tion of the structural parameters is obtained as shown inFigure 6 It is clear from Figure 6 that the structure parame-ters are Re1 = 90mm Re2 = 70mm and Re3 = 30mm and the

probability model of the structural parameters of the biomi-metic robotic elbow joint is higher

5 The Design of the Biomimetic RoboticElbow Joint

Considering its processing and assembling process the vir-tual prototype of the elbow joint is designed based on theoptimized structure parameters and primary technicalparameters are shown in Table 1

The virtual prototype model of the biomimetic roboticelbow joint is shown in Figure 7

Servo motor 13 is installed on motor base 15 and servomotor 13 transmits the torque of the motor to carrier rod23 through the planar four-bar mechanism The other move-ment branch of the biomimetic robotic elbow joint is servomotor 7 mounted on elbow base 5 Servo motor 7 is fixedlyconnected with the rotating shaft on the bottom of connect-ing rod 17 through the mounting hole of coupling 8 Con-necting rod 17 is connected to annular member 21 by apair of coaxial rotating hinges 18 and 19 The other pair ofcoaxial rotary hinges 26 and 27 on annular member 21 is

60 70 80 900

02

04

06

08

ne (R

e1)

Re1 (mm)

(a) The probability of Re1

ne (R

e2)

40 50 60 700

02

04

06

08

Re2 (mm)

(b) The probability of Re2

ne (R

e3)

20 30 40 500

02

04

06

08

Re3 (mm)

(c) The probability of Re3

Figure 6 Probability distribution of the discrete histogram for the structure parameters for the biomimetic robotic elbow joint

Table 1 The primary technical parameters of the biomimeticrobotic elbow joint

Design parameter Technical index

Degree of freedom 2

Flexion 45deg

Extension 45deg

Internal rotation 50deg

External rotation 45deg

Re1 90mm

Re2 70mm

Re3 30mm

Motor Maxon 273755

Coupling Maxon 326665

Encoder MR TL 256-1024 CPT


connected to moving platform 22 Arm connector 24 isfixedly connected to the bottom of the moving platform

6 Simulation Experimental Analyses

61 Kinematic Simulation Experiment In order to verify thecorrectness of the kinematic equations of the elbow jointmechanism the results of the theoretical solution of theelbow joint and the simulation of the kinematic model arecompared and analyzed The movement trajectory of the bio-mimetic robotic elbow joint moving platform is expressed by

γe = sin t rad βe = cos t rad

21

According to (11) under a given movement trajectorythe theoretical input angular velocity curve can be obtainedby using MATLAB as shown in Figure 8 A virtual prototypeof the elbow joint is designed based on the optimized struc-ture parameters and the simulation value of the movementchange curve of the input angle of the virtual prototype isobtained by using ADAMS movement simulation softwareas shown in Figure 8 From Figure 8 the theoretical valuesand the simulation values are almost identical which verifiesthe correctness of the modeling of the movement equation

62 Kinematic Decoupling Simulation Experiment A virtualprototype of the biomimetic robotic elbow joint is estab-lished and a virtual simulation experiment is performedBased on the Core software the elbow joint is parametricdesigned The parameter design range is the same as theparameter range in the spatial model theory The parametric

design variable increment is 5mm and 343 virtual proto-types of elbow joints with different structural dimensionswere obtained

The kinematic simulation of the reachable workspace iscarried out for each prototype and the total volume numberof workspaces and the number volume of workspaces con-forming to the kinematic decoupling index are recorded

The structural parameters were obtained by optimizingthe spatial model which are 30mm 70mm and 90mmThe kinematic decoupling workspace volume number istaken as the standard value Wd0 and the virtual prototypeis defined by the standard prototype The volume numberof kinematic decoupling workspaces obtained by other differ-ent structural parameters is Wd The kinematic decouplingworkspace volume ratio Wds is defined as

Wds = WdWd0

times 100 22

The 343 elbow joint movement decoupling volume num-bers are compared with the basic kinematic decoupling vol-ume number When one structural parameter is changedand the other parameters are unchanged in the standardprototype the volume number of kinematic decouplingworkspaces is acquired and the influence curve of each struc-tural parameter on the size of the elbow joint kinematicdecoupling workspace is drawn as shown in Figure 9

In Figure 9 the kinematic decoupling volume ratio Wdsincreases with the increase of Re2 and Re3 and with theincrease of Re3 the volume ratio of the kinematic decouplingworkspace firstly increases and then decreases The changetrend is the same as that in Figure 6 the rationality of optimi-zation of the structural parameters can be proved and thekinematic decoupling analysis is correct

7 Conclusion

The kinematic decoupling analysis of a novel biomimeticrobotic elbow joint was performed Analysis of the kinematicdecoupling of the elbow joint is symmetrical in the work-space and the motion is completely decoupling when drivenby a single motor The global kinematic decoupling perfor-mance of the elbow joint showed a linear distribution With

1

4

7 8

9

13 14

15

1718 19

2122

24

23

5

6

1011

12

16

20

23

26 27 25

1

Figure 7 A novel biomimetic robotic elbow joint virtual prototype1 3 9 11 16 18 19 20 25 26 and 27mdashrevolute joints 2 and10mdashshort bars 4mdashframe 5mdashupper arm 6mdashlong bar 7 and13mdashmotor 8 and 14mdashconnectors 12ndash15mdashmotor bases 17 and23mdashconnecting rods 21mdashannular member 22mdashmoving platformand 24mdasharm connector

150 5 10

Inpu

t ang

le v

eloci

ty120576 e

(rad

s)

0

1

1

2

2

120576e1120576e2

120576e1120576e2

Time t (s)

Theory value Simulation value

Figure 8 The input angle velocity curve of the elbow joint


the increase of Re3 the decoupling decreased gradually Thestructure parameters of the elbow joint were selected by theMonte Carlo method which areRe1 = 90mm Re2 = 70mmand Re3 = 30mm Considering the process and the assemblyprocess the elbow joint prototype had been designed anddeveloped Finally simulation experiments have verified thecorrectness of the kinematic equation and kinematic decou-pling as well as the rationality of the optimization use ofspatial model parameters

In summary the biomimetic robotic elbow joint hastwo degrees of freedom and good decoupling characteris-tics which can be applied in rehabilitation robot biomi-metic robot industrial robot humanoid robot arm andother fields

Conflicts of Interest

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported by the Chinese National NaturalScience Fund (E51505124) Hebei Provincial Natural ScienceFoundation (E2017209252) Department of Education ofHebei Province (QN2015203 and 2015GJJG084) and OnlineEducation Research Fund of Education Research Center ofthe Ministry of Education (2016YB117)

References

[1] H-Y Xu Y-L Fu S-G Wang and J-G Liu ldquoResearch onbiomimetic roboticsrdquo Robot vol 26 no 3 pp 283ndash288 2004

[2] G Wang D Chen K Chen and Z Zhang ldquoThe currentresearch status and development strategy on biomimetic

robotrdquo Journal of Mechanical Engineering vol 51 no 13pp 27ndash44 2015

[3] L D Paulson ldquoBiomimetic robotsrdquo Computer vol 37 no 9pp 48ndash53 2004

[4] Y Lu ldquoThe significance and development of bionicsrdquo ScientificChinese vol 4 pp 22ndash24 2004

[5] B Tondu ldquoModelling of the shoulder complex and applicationto the design of upper extremities for humanoid robotsrdquo in 5thIEEE-RAS International Conference on Humanoid Robots2005 pp 313ndash320 Tsukuba Japan December 2005 IEEE

[6] B Tondu ldquoKinematic modelling of anthropomorphic robotupper limb with human-like handsrdquo in 2009 InternationalConference on Advanced Robotics pp 1ndash9 Munich GermanyJune 2009 IEEE

[7] S Hong C Cho H Lee S Kang and W Lee ldquoJoint configu-ration for physically safe humanndashrobot interaction of serial-chain manipulatorsrdquo Mechanism and Machine Theoryvol 107 pp 246ndash260 2017

[8] Y B Li Z L Jin S M Ji and F Gao ldquoError analysis of aparallel anthropopathic shoulderrdquo Journal of Basic Scienceand Engineering vol 17 no 3 pp 446ndash451 2009

[9] C Li S Xie H Li D Wang and J Luo ldquoDesign of bionic eyebased on spherical parallel mechanism with optimized param-etersrdquo Robot vol 32 no 6 pp 781ndash786 2010

[10] J Klein S Spencer J Allington J E Bobrow and D J Rein-kensmeyer ldquoOptimization of a parallel shoulder mechanismto achieve a high-force low-mass robotic-arm exoskeletonrdquoIEEETransactions onRobotics vol 26 no 4 pp 710ndash715 2010

[11] L Zhang and Z Jin ldquoAnalysis on driving characteristics of arobot shoulder joint based on parallel mechanismrdquo EnergyEducation Science and Technology Part A Energy Science andResearch vol 32 no 6 pp 5073ndash5080 2014

[12] L Sun Y Liu and Y Zhu ldquoPosition analysis of a spherical3-DOF parallel decoupling mechanism for wrist joints ChinardquoMechanical Engineering vol 14 no 10 pp 0831ndash0834 2003

[13] B Cui and Z Jin ldquoAnalysis of statics performance for a novelelbow joint of agricultural robotrdquo Transactions of the Chinese

30

50

70

90

110

60 70 80 9040 50 60 7020 30 40 50

Wds

(100

)

Re1Re2Re3

(mm)Re1Re2Re3

Figure 9 The influence curve of structural parameters on the kinematic decoupling workspace volume ratio


Society of Agricultural Engineering vol 27 no 3 pp 122ndash1252011

[14] B Cui L Chen Z Wang Y Zhao Z Li and Z Jin ldquoDesignand dynamic analysis of a novel biomimetic robotics hipjointrdquo Applied Bionics and Biomechanics vol 2015 ArticleID 145040 8 pages 2015

[15] X Xu L Hou X Huang andW Zhang ldquoDesign and researchof a wearable robot for upper limbs rehabilitation based onexoskeletonrdquo Robot vol 2 p 003 2014

[16] G S Luo J W Chen and L Y Gu ldquoAn elbow of 7-DOFhydraulic manipulator based on double-screw-pair transmis-sionrdquo Robot vol 36 no 1 pp 36ndash43 2014

[17] M Hwang U-J Yang D Kong et al ldquoA single port surgicalrobot system with novel elbow joint mechanism for high forcetransmissionrdquo The International Journal of Medical Roboticsand Computer Assisted Surgery vol 13 no 4 2017

[18] M M Stanišić and C M Goehler ldquoReproducing human armmotion using a kinematically coupled humanoid shoulderndashelbow complexrdquo Applied Bionics and Biomechanics vol 5no 4 185 pages 2008

[19] E-C Lovasz D T Mărgineanu V Ciupe et al ldquoDesign andcontrol solutions for haptic elbow exoskeleton module usedin space teleroboticsrdquo Mechanism and Machine Theoryvol 107 pp 384ndash398 2017

[20] H Zou and F Gao Progress of Modern Mechanism HigherEducation Press Beijing China 2007

[21] J Gong Y Zhang and F Gao ldquoDecoupling characteristics ofparallel mechanismrdquo The Mechanical Engineering of Chinavol 17 no 14 pp 1509ndash1511 2006

[22] H Shen L Ma X Zhu and T Yang ldquoAnalyses of kinematicsand workspace for a 3-DOF fully decoupled parallel mecha-nismrdquo Transactions of the Chinese Society of AgriculturalMachinery vol 36 no 11 pp 130ndash133 2005

[23] Y Xu D Zhang J Yao and Y Zhao ldquoType synthesis of the2R1T parallel mechanism with two continuous rotational axesand study on the principle of its motion decouplingrdquo Mecha-nism and Machine Theory vol 108 pp 27ndash40 2017

[24] T Essomba and L Nguyen Vu ldquoKinematic analysis of a newfive-bar spherical decoupled mechanism with two-degrees offreedom remote center of motionrdquo Mechanism and MachineTheory vol 119 pp 184ndash197 2018

[25] B Y Cui and L W Chen ldquoAnalysis of kinematics and designof structure parameters for a bionic parallel legrdquo Journal ofBiomimetics Biomaterials and Biomedical Engineering vol 20pp 23ndash33 2014

[26] B Y Cui L W Chen Y T Xie and Y D Hu ldquoStatic decou-pling performance analysis and design of bionic elbow jointrdquoJournal of Biomimetics Biomaterials and Biomedical Engineer-ing vol 36 pp 34ndash44 2018

[27] S-D Stan M Manic V Maties and R Balan ldquoEvolutionaryapproach to optimal design of 3 DOF translation exoskeletonand medical parallel robotsrdquo in 2008 Conference on HumanSystem Interactions pp 720ndash725 Krakon Poland May 2008

[28] Y B Li Z L Jin and S M Ji ldquoDesign of a novel 3-DOF hybridmechanical armrdquo Science in China Series E TechnologicalSciences vol 52 no 12 pp 3592ndash3600 2009


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018


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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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SensorsJournal of



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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


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Submit your manuscripts atwwwhindawicom

proposed a wrist joint based on a spherical 3-DOF paralleldecoupling mechanism and the position of the wrist jointwas analyzed

Cui and Jin [13] presented a 2-DOF elbow joint definedthe static performance index and obtained the static perfor-mance curve In 2015 a novel hip joint is designed and itsdynamic characters and structural parameters have studied[14] Xu et al [15] designed an elbow joint based on largedeceleration ratio traction motor direct drive structure andanalyzed the force character and the elbow provided effectiveflexion and extension movement based on the double-screw-pair transmission and the elbow joint developed and com-pleted flexion and extension movement [16] Hwang et al[17] proposed a novel elbow based on a slider-crank mecha-nism and obtained the force transmission property curveStanišić and Goehler [18] proposed a hybrid shoulder mech-anism for copying the grasping movement and a mechanismcapable of reproducing voluntary human reaching motions isintroduced along with the procedural method of implement-ing the coupled motions Lovasz et al [19] designed an elbowmodule carried on remote control for a haptic arm exoskel-eton and proposed several design solutions and a controlstrategy A biomimetic robotic elbow joint plays a very signif-icant role in the motion control of a biomimetic roboticmanipulator The kinematic decoupling is an importantindex which affects the overall motion and the control ofthe biomimetic robotic elbow joint The kinematic decou-pling of the mechanism [20] can determine its kinematiccharacteristics and provide the basis for the robot controland trajectory planning

The problem of decoupling is closely related to theJacobian matrix of the biomimetic robotic joint Researchershave studied less in this field Gong et al [21] proposed thedecoupling of the moving coordinates in the absolute coordi-nates and verified the decoupling theory by the correspond-ing examples Shen et al [22] analyzed the kinematicdecoupling of a 6-DOF parallel mechanism Xu et al [23]studied the 2R1T parallel mechanism on the principle of itsmotion decoupling based on the positional relationshipbetween the actuation force and the rotational axis Essombaand Nguyen Vu [24] presented a novel spherical decoupledmechanism and proved the decoupling motion by itskinematic and velocity models

Based on the analysis of the literature the existing roboticelbow joint is usually able to achieve flexion and extensionThe structure of elbow joint design adopts a series structurethe series structure lacks good centering ability From theanalysis of the performance of elbow joints there are manyliteratures on the bearing capacity of elbow joints and the lit-erature of the kinematic decoupling has not been seen yet Onthis basis this paper proposes a biomimetic robotic elbowjoint The biomimetic robotic elbow joint adopts a 2-DOFspherical parallel mechanism as a prototype which hasadvantages of good structural characteristics large range ofmotion and high bearing capacity and was compared withthe 3-DOF parallel mechanism in the 863 project From theanalysis of the degree of freedom of the mechanism the3-DOF spherical parallelmechanismhas three degrees of free-dom in accordance with the requirements of the prosthetic

prototype of the shoulder joint and the human elbow jointstructure has two degrees of freedom of movement character-istics so the elbow joint mechanism has very good bionicstructure From the analysis of the installation of the mecha-nism the rotation center of the 3-DOF spherical parallelmechanism is located in the middle of the moving platformand the static platform The neutrality requirements for therods during installation are very high and difficult to installThe rotation center of each rod of the biomimetic roboticelbow joint presents 90 degrees which is convenient to installand has good neutrality

In this paper the kinematic equation of the biomi-metic robotic elbow joint is established the Jacobianmatrix is derived the kinematic decoupling performanceevaluation index of the biomimetic robotic elbow joint isdefined the kinematic decoupling performance evaluationindex map is drawn in the workspace and the global kine-matic decoupling performance index is established basedon the kinematic decoupling analysis Based on the spacemodel theory the structural parameters of the elbow jointare optimized and selected by the Monte Carlo methodand the biomimetic robotic elbow joint is designed Thepurpose of the decoupling analysis of the elbow joint isto make the control of the elbow joint mechanism moreconvenient and easier

2 The Model and Position Analysis

21 The Structural Description The biomimetic roboticelbow joint is an important joint of the biomimetic handOn the base of the knowledge of bionics the human elbowjoint is composed of the humerus radius ulna and ligamentThe human elbow joint is limited to the connection betweenthe three bones and the ligament which can only rotateabout two axes and can realize movement of internal rotationand external rotation and flexion and extension as shown inFigure 1

The structure design of the biomimetic robotic elbowjoint should be able to realize the movement of theanthropomorphic elbow joint According to the analysisof joint structure and kinematic characteristics of thehuman elbow joint this paper proposed a novel biomi-metic robotic elbow joint based on a 2-DOF orthogonalspherical parallel mechanism The elbow joint has two

Humerus

UlnaLigament

Radius

Figure 1 Schematic diagram of the human elbow joint







=

cos βe 0 sin βe



1


ℓ2 = Te

010

=0

cos γesin γe

2



0 sin εe1 cos εe1

010

=0cos εe1sin εe1

3


εe1 = γe 4


ℓ3 = Te

100

=cos βe

sin γesin βe

minussin γecos βe

5




001

=sin εe2

0cos εe2

6


ℓ1 sdot ℓ3 = 0 7





9

Ae1

Ae2

Xe

Ye

Ae3

Ae4

Ze

Ae5

Oe

9857474

9857475

9857473

98574719857472

ix

yi

iz

Ae6

Ae7

Ae8minus9857471

minus9857475

minus9857473

1

2

3 64 5

120576e2

120576e1





10



ϕe = Jeεe 11




extracted as

Je =1 0



12



ςe max 13





Je =1 00 1

14








035030025020015010005

050

minus50 minus50

500 0

e (120596

e)

120573e (deg)120574e (deg)




le =Re1 + Re2 + Re3

3 15


le1 =Re1le

le2 =Re2le

le3 =Re3le

16


le1 + le2 + le3 = 3 17



18




y = le3

19


ξe =VeweierpedV e

VedVe

20




0

3

3

3le1

le3

le2

Pe

Qe

Se


model

3

x

y

3

15

le1

le3

le2

Qe

Se

Pe0

0

0



3x

y

3

15

0

0010

015020

025

005

le1

le3

le2

Se

Pe0 Qe













60 70 80 900

02

04

06

08

ne (R

e1)

Re1 (mm)


ne (R

e2)

40 50 60 700

02

04

06

08

Re2 (mm)


ne (R

e3)

20 30 40 500

02

04

06

08

Re3 (mm)





Degree of freedom 2

Flexion 45deg

Extension 45deg



Re1 90mm

Re2 70mm

Re3 30mm

Motor Maxon 273755








21






Wds = WdWd0

times 100 22



7 Conclusion


1

4

7 8

9

13 14

15

1718 19

2122

24

23

5

6

1011

12

16

20

23

26 27 25

1


150 5 10

Inpu

t ang

le v

eloci

ty120576 e

(rad

s)

0

1

1

2

2

120576e1120576e2

120576e1120576e2

Time t (s)








Acknowledgments


References















30

50

70

90

110

60 70 80 9040 50 60 7020 30 40 50

Wds

(100

)

Re1Re2Re3

(mm)Re1Re2Re3






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







=

cos βe 0 sin βe



1


ℓ2 = Te

010

=0

cos γesin γe

2



0 sin εe1 cos εe1

010

=0cos εe1sin εe1

3


εe1 = γe 4


ℓ3 = Te

100

=cos βe

sin γesin βe

minussin γecos βe

5




001

=sin εe2

0cos εe2

6


ℓ1 sdot ℓ3 = 0 7





9

Ae1

Ae2

Xe

Ye

Ae3

Ae4

Ze

Ae5

Oe

9857474

9857475

9857473

98574719857472

ix

yi

iz

Ae6

Ae7

Ae8minus9857471

minus9857475

minus9857473

1

2

3 64 5

120576e2

120576e1





10



ϕe = Jeεe 11




extracted as

Je =1 0



12



ςe max 13





Je =1 00 1

14








035030025020015010005

050

minus50 minus50

500 0

e (120596

e)

120573e (deg)120574e (deg)




le =Re1 + Re2 + Re3

3 15


le1 =Re1le

le2 =Re2le

le3 =Re3le

16


le1 + le2 + le3 = 3 17



18




y = le3

19


ξe =VeweierpedV e

VedVe

20




0

3

3

3le1

le3

le2

Pe

Qe

Se


model

3

x

y

3

15

le1

le3

le2

Qe

Se

Pe0

0

0



3x

y

3

15

0

0010

015020

025

005

le1

le3

le2

Se

Pe0 Qe













60 70 80 900

02

04

06

08

ne (R

e1)

Re1 (mm)


ne (R

e2)

40 50 60 700

02

04

06

08

Re2 (mm)


ne (R

e3)

20 30 40 500

02

04

06

08

Re3 (mm)





Degree of freedom 2

Flexion 45deg

Extension 45deg



Re1 90mm

Re2 70mm

Re3 30mm

Motor Maxon 273755








21






Wds = WdWd0

times 100 22



7 Conclusion


1

4

7 8

9

13 14

15

1718 19

2122

24

23

5

6

1011

12

16

20

23

26 27 25

1


150 5 10

Inpu

t ang

le v

eloci

ty120576 e

(rad

s)

0

1

1

2

2

120576e1120576e2

120576e1120576e2

Time t (s)








Acknowledgments


References















30

50

70

90

110

60 70 80 9040 50 60 7020 30 40 50

Wds

(100

)

Re1Re2Re3

(mm)Re1Re2Re3






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




10



ϕe = Jeεe 11




extracted as

Je =1 0



12



ςe max 13





Je =1 00 1

14








035030025020015010005

050

minus50 minus50

500 0

e (120596

e)

120573e (deg)120574e (deg)




le =Re1 + Re2 + Re3

3 15


le1 =Re1le

le2 =Re2le

le3 =Re3le

16


le1 + le2 + le3 = 3 17



18




y = le3

19


ξe =VeweierpedV e

VedVe

20




0

3

3

3le1

le3

le2

Pe

Qe

Se


model

3

x

y

3

15

le1

le3

le2

Qe

Se

Pe0

0

0



3x

y

3

15

0

0010

015020

025

005

le1

le3

le2

Se

Pe0 Qe













60 70 80 900

02

04

06

08

ne (R

e1)

Re1 (mm)


ne (R

e2)

40 50 60 700

02

04

06

08

Re2 (mm)


ne (R

e3)

20 30 40 500

02

04

06

08

Re3 (mm)





Degree of freedom 2

Flexion 45deg

Extension 45deg



Re1 90mm

Re2 70mm

Re3 30mm

Motor Maxon 273755








21






Wds = WdWd0

times 100 22



7 Conclusion


1

4

7 8

9

13 14

15

1718 19

2122

24

23

5

6

1011

12

16

20

23

26 27 25

1


150 5 10

Inpu

t ang

le v

eloci

ty120576 e

(rad

s)

0

1

1

2

2

120576e1120576e2

120576e1120576e2

Time t (s)








Acknowledgments


References















30

50

70

90

110

60 70 80 9040 50 60 7020 30 40 50

Wds

(100

)

Re1Re2Re3

(mm)Re1Re2Re3






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



le =Re1 + Re2 + Re3

3 15


le1 =Re1le

le2 =Re2le

le3 =Re3le

16


le1 + le2 + le3 = 3 17



18




y = le3

19


ξe =VeweierpedV e

VedVe

20




0

3

3

3le1

le3

le2

Pe

Qe

Se


model

3

x

y

3

15

le1

le3

le2

Qe

Se

Pe0

0

0



3x

y

3

15

0

0010

015020

025

005

le1

le3

le2

Se

Pe0 Qe













60 70 80 900

02

04

06

08

ne (R

e1)

Re1 (mm)


ne (R

e2)

40 50 60 700

02

04

06

08

Re2 (mm)


ne (R

e3)

20 30 40 500

02

04

06

08

Re3 (mm)





Degree of freedom 2

Flexion 45deg

Extension 45deg



Re1 90mm

Re2 70mm

Re3 30mm

Motor Maxon 273755








21






Wds = WdWd0

times 100 22



7 Conclusion


1

4

7 8

9

13 14

15

1718 19

2122

24

23

5

6

1011

12

16

20

23

26 27 25

1


150 5 10

Inpu

t ang

le v

eloci

ty120576 e

(rad

s)

0

1

1

2

2

120576e1120576e2

120576e1120576e2

Time t (s)








Acknowledgments


References















30

50

70

90

110

60 70 80 9040 50 60 7020 30 40 50

Wds

(100

)

Re1Re2Re3

(mm)Re1Re2Re3






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












60 70 80 900

02

04

06

08

ne (R

e1)

Re1 (mm)


ne (R

e2)

40 50 60 700

02

04

06

08

Re2 (mm)


ne (R

e3)

20 30 40 500

02

04

06

08

Re3 (mm)





Degree of freedom 2

Flexion 45deg

Extension 45deg



Re1 90mm

Re2 70mm

Re3 30mm

Motor Maxon 273755








21






Wds = WdWd0

times 100 22



7 Conclusion


1

4

7 8

9

13 14

15

1718 19

2122

24

23

5

6

1011

12

16

20

23

26 27 25

1


150 5 10

Inpu

t ang

le v

eloci

ty120576 e

(rad

s)

0

1

1

2

2

120576e1120576e2

120576e1120576e2

Time t (s)








Acknowledgments


References















30

50

70

90

110

60 70 80 9040 50 60 7020 30 40 50

Wds

(100

)

Re1Re2Re3

(mm)Re1Re2Re3






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






21






Wds = WdWd0

times 100 22



7 Conclusion


1

4

7 8

9

13 14

15

1718 19

2122

24

23

5

6

1011

12

16

20

23

26 27 25

1


150 5 10

Inpu

t ang

le v

eloci

ty120576 e

(rad

s)

0

1

1

2

2

120576e1120576e2

120576e1120576e2

Time t (s)








Acknowledgments


References















30

50

70

90

110

60 70 80 9040 50 60 7020 30 40 50

Wds

(100

)

Re1Re2Re3

(mm)Re1Re2Re3






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Acknowledgments


References















30

50

70

90

110

60 70 80 9040 50 60 7020 30 40 50

Wds

(100

)

Re1Re2Re3

(mm)Re1Re2Re3






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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