CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 29,aNo. 4,a2016

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DOI: 10.3901/CJME.2016.0413.051, available online at www.springerlink.com; www.cjmenet.com

Mechanics Unloading Analysis and Experimentation of a New Type of Parallel Biomimetic Shoulder Complex HOU Yulei, LI Zhisen, WANG Yi, ZHANG Wenwen, ZENG Daxing, and ZHOU Yulin* School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China Received August 5, 2015; revised March 23, 2016; accepted April 13, 2016

Abstract: The structure design for high ratio of carrying capacity to deadweight is one of the challenges for the bionic mechanism, while the problem concerning high carrying capacity has not yet be solved for the existing shoulder complex. A new type biomimetic shoulder complex, which adopts 3-PSS/S(P for prismatic pair, S for spherical pair) spherical parallel mechanism (SPM), is proposed. The static equilibrium equations of each component are established by using the vector method and the equations for constrain forces with certain load are solved. Then the constrain force on the middle limb and that on the side limbs are compared in order to verify the unloading performance of the mechanism. In addition, the prototype mechanism of the shoulder complex is developed, and the force feedback experiment is conducted to verify the static analysis, which indicates that the middle limb suffers most of the external force and the effect of mechanics unloading is achieved. The 3-PSS/S spherical parallel mechanism is presented for the shoulder complex, and the realization of mechanics unloading is benefit for the improvement of the carrying capacity of the shoulder complex. Keywords: biomimetic shoulder complex, humanoid robot, spherical parallel mechanism, carrying capacity, mechanics unloading

1

Introduction

In recent years, the research on the bionic robot[1–2], which is the robot system that imitates the delicate structure, movement principle and behavior of organisms in nature, has become a hot research topic in the robot fields. The humanoid robot[3–4] is an important branch of the field of bionic robot, and the structure and function of the humanoid robot joint decide the overall performance directly. As we know, the shoulder complex has good flexibility and possesses the largest range of movement in the human body[5], which is the most sophisticated part in terms of degrees of freedom and motion[6]. Combining the advantages of the parallel mechanism and the cable driven, LIU, et al[7], proposed a bionic shoulder joint robot with a spherical hinge which is driven by a group of pneumatic artificial muscle. PARK, et al[8], introduced a passive shoulder joint tracking device for upper limb rehabilitation robots which was characterized by light weight and low cost. IKEMOTO, et al[9], proposed a linkage mechanism that can reproduce complex three-dimensional scapulo * Corresponding author. E-mail: [email protected] Supported by National Natural Science Foundation of China(Grant No. 51275443), Key Project of Ministry of Education of China(Grant No. 212012), Hebei Provincial Natural Science Foundation of China(Grant No. E2012203034), Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No. 20111333120004), and Research Fund for Outstanding Youth in Higher Education Institutions of Hebei Province, China(Grant No. Y2011114) © Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2016

movements and presented experiments in which the robot was controlled by surface electromyographic signals from a human. VRIES, et al[10], presented the use of a neural network for the prediction of glenohumeral joint reaction forces based upon arm kinematics and shoulder muscle electromyogram, which was promising and enabled long term estimation of shoulder joint reaction forces. Three degrees of freedom(DOFs) SPM, the structure and function of which is very similar to that of the shoulder complex, is one of the typical less degrees of freedom parallel mechanism[11–12], and is very suitable to be the shoulder complex prototype mechanism of the humanoid robot. ZHANG, et al[13], proposed a 3-DOF robot shoulder joint and studied its driving characteristics combining the velocity Jacobian matrix with virtual displacement principle. LO, et al[14], presented an upper limb rehabilitation exoskeleton with an optimized 4R spherical wrist mechanism for the shoulder joint, which allowed the exoskeleton to achieve the entire human shoulder workspace without mechanical interference. LU, et al[15], established the mathematical relationships between the suffered external torque of platform and the output torque required by three cranks with component vector method, and performed the force feedback control experiments of 3-RSS/S parallel mechanism which verify that the static analysis model of parallel mechanism can be used as the theoretical basis of the force control under low-speed conditions. GAN, et al[16], presented a systematic method in modeling kinematics, singularity and workspace analysis which provides optimization design index and a simpler

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HOU Yulei, et al: Mechanics Unloading Analysis and Experimentation of a New Type of Parallel Biomimetic Shoulder Complex

kinematics model for dynamics and control of linear-actuated symmetrical spherical parallel manipulators. LI, et al[17], proposed a bionic eyes system of active compensation for robot visual error by using a spherical parallel mechanism and performed the optimization by taking the worst-case performance index as the target. The flexibility and the carrying capacity are closely related. High carrying capacity is an important premise to ensure the flexibility of the shoulder complex. As one of the challenges for the bionic mechanism, the structure design of high ratio of carrying capacity to deadweight is worth focusing on. Then for the performance evaluation of the shoulder complex, the high carrying capacity is one of important indices, and should be considered particularly. The shoulder complex[18–19] inevitably bears certain strength of force and torque while working. However, the external force of the 3-RRR SPM[20], for the reason of the structure, can’t be balanced by the input torque. Therefore the additional load will be produced in the parallel limbs. Then the additional load will cause a series of problems, such as resulting in the deformation of the parallel limbs, increasing friction of the kinematic pair, and reducing the efficiency and accuracy. The problems above will seriously restrict the application of the 3-RRR SPM. Therefore, mechanics unloading, which can reduce all or most force that the external force applied on the parallel limbs, is necessary. Then the 3-PSS/S SPM is proposed for the prototype mechanism of the human shoulder complex. Based on the vector method[21], this paper analyzes the statics of the 3-PSS/S SPM and compares the constrain forces with attitude angle on the middle limb to that on other limbs. Furthermore, the force feedback experiment is conducted to test the mechanics unloading performance of the shoulder complex.

Fig. 1. Model of the 3-PSS/S spherical parallel shoulder complex

Fig. 2. Schematic diagram of the 3-PSS/S spherical parallel mechanism

The coordinate vector of point Ai in the stationary coordinate system can be represented as Ai = [ Si s i ci

2

Kinematics Analysis of the Shoulder Complex

As shown in Fig. 1, the 3-PSS/S spherical parallel shoulder complex mechanism comprises a moving platform, a fixed base, three side limbs (PSS) and a middle limb[22]. The input variable of the mechanism, denoting as (S1, S2, S3), is the distance from the spherical pair Ai (i=1, 2, 3) to point O, which is the intersection of the three slide way in the side limbs. As Fig. 2 shown, the stationary coordinate system O-XYZ (denoted as {F}) of the 3-PSS/S SPM is set up with its origin located at O. Z axis is along OO1 and up is taken to be the positive direction, X axis is in the plane determined by Z axis and OA1, and the direction towards A1 is taken to be the positive direction. The moving coordinate system O1-uvw (denoted as {M}) is established with its origin located at O1, the w axis is normal to the moving platform and up is taken to be the positive direction, u axis is along the same direction with O1B1.

S i s i s i

T

- Si c i ] , i = (1, 2, 3),

(1)

where  i is the angle between Z axis negative direction and O1Ai, i is the angle between X axis positive direction and the projection of O1Ai in the XY plane ( 1 = 0 , 2 = 2π / 3 , 3 = 4π / 3 ), s i means sin  i , c i means cos  i , the rest is similar. The coordinate vector of point Bi in the moving coordinate system can be represented as T

Bi¢ = éë L2 s 2¢ci¢ L2 s 2¢si¢ L2 c 2¢ ùû , i = (1, 2, 3),

(2)

where θ2¢ is the angle between w axis positive direction and O1Bi (in this paper, all the spherical pair connecting with the moving platform are on the same plane, so θ2¢ = 90 ), hi¢ is the angle between u axis and the projection of O1Bi in the uv plane( 1¢ = 0 , 2¢ = 2π / 3 , 3¢ = 4π / 3 ), L2 = O1 Bi . Bi¢ in the stationary coordinate system can be expressed as

CHINESE JOURNAL OF MECHANICAL ENGINEERING Bi¢ =

F ¢ M RBi + O1O

= [ ai

bi

T

ci + h ] , i = (1, 2, 3), (3)

where h = OO1 , MF R is the transformation matrix from the moving coordinate system to the stationary coordinate system, can be expressed as

æc c ç  c çç è -s

çç F s M R =ç ç

c s s - s c s s s + c c c s

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c s c + s s ö÷ ÷ s s c - c s ÷÷÷ , ÷÷ ÷ø c c

ai = L2 (c c ci + c s s si - s c si ) , bi = L2 (s c ci + s s s si + s c si ) , ci = L2 (-s ci + c s si ) . The distance between the two spherical pairs in the side limbs can be expressed as

Ai - Bi = l , i = (1, 2, 3) ,

3.1 Static analysis of the moving platform The moving platform connects the side limbs with the spherical pair, and the side limbs PSS possess six degrees of freedom and have no constraints on the moving platform, so each of the side limbs only bear the constraint force denoted as FBi without the constraint torque. And the force that the middle limb supporting the moving platform is denoted as FN. For the convenience of the mathematical modeling and emulation, all of forces or torques on the moving platform are expressed in the stationary coordinate system {F}. Then FBi=(FBix, FBiy, FBiz)T, three projections of FBi on each fixed axis are FBix, FBiy, and FBiz respectively, FN=(FNx, FNy, FNz)T, the projections of FN on each fixed axis are FNx, FNy and FNz respectively. Gravity Go=(0, 0, –mog)T, –mog means Go is contrary to Z-axis positive direction while mo is the quality of moving platform. The force analysis is shown in Fig. 3.

(4)

where l = Ai Bi . By substituting Eq. (2) and Eq. (3) into Eq. (4), the following equation can be derived: Si = (ai m1i + bi m2i - ei m3i )  l 2 - éê (ui ) 2 + (vi ) 2 + ( wi ) 2 ùú , ë û i = (1, 2, 3) , (5)

where

m1i = s i ci ,

Fig. 3.

When the moving platform is in equilibrium state, the force equilibrium equation can be expressed as

m2i = s i si , m3i = c 1 ,

3

å FBi + FN + F + Go = 0,

ei = ci + h , ui = ai m2i - bi m1i ,

(7)

Then Eq. (7) can be rewrited into scalar expression as

wi = bi m3i + ei m2i .

Establishment of Static Equilibrium Equations of the Shoulder Complex

To facilitate the analysis, the friction between the kinematic pairs is ignored tentatively. In a general sense, a composite six dimensional force vector is applied on the moving platform of the shoulder complex, and denoted as æF ö Fw = çç ÷÷÷ , çè M ÷ø

i = (1, 2, 3).

i=1

vi = ai m3i + ei m1i ,

3

Force analysis of the moving platform

(6)

where F=(–Fx, –Fy, –Fz )T, –Fx means the projection of F on X-axis is contrary to X-axis positive direction when Fx>0, or else is opposite; M=(–Mx, –My, –Mz)T, –Mx means the torque is an anti-clockwise moment about X-axis when Mx>0, or else is opposite.

3 ì ï ï ï å FBxi + FNx - Fx = 0, ï ï i =1 ï ï 3 ï ï F + F - F = 0, i = (1, 2, 3). (8) íå Byi Ny y ï i =1 ï ï ï 3 ï ï FBzi + FNz - Fz - mo g = 0, ï å ï ï î i=1 Choosing the geometry center of the moving platform to be employed in evaluating the torques, the torque equilibrium equation of the moving platform can be expressed as 3

å O1 Bi ´ FBi + M = 0,

i = (1, 2, 3),

i=1

where

O1 Bi =(ai , bi , ci )T .

Eq. (9) can be translated into scalar expression as

(9)

HOU Yulei, et al: Mechanics Unloading Analysis and Experimentation of a New Type of Parallel Biomimetic Shoulder Complex

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3 ì ï ï ( FBzi bi - FByi ci ) - M x = 0, ï å ï ï i =1 ï ï 3 ï ï íå ( FBxi ci - FBzi ai ) - M y = 0, i = (1, 2, 3). ï i =1 ï ï ï 3 ï ï ï å ( FByi ai - FBxi bi ) - M z = 0, ï ï î i=1

1 Ai Bi ´ FBi¢ + Ai Bi ´Gl = 0, i = (1, 2, 3), 2 (10)

Static analysis of the connecting rod in the side limbs Each of the connecting rod in the side limbs connects the moving platform and the sliders with the spherical pair, so the side limbs only bear the constrain forces from the moving platform and the sliders besides gravity

Gl = (0, 0, - ml g) . ml

is quality of the moving

platform. In the stationary coordinate system {F}, the constrain forces on the side limb from the moving platform ¢ , - FBiy ¢ , - FBiz ¢ )T can be denoted as FBi¢ = (-FBix

¢ , i = (1, 2, 3) , which is the reacting force of FBi . FBix ¢ and FBiz ¢ are three projections of FBi¢ on each fixed FBix axis. The constrain force on the side limb from the sliders denoted as FAi = ( FAix , FAiy , FAiz )T (i=1, 2, 3), FAix , FAiy and FAiz are three projections of FAi on each

fixed axis. Defining Ai Bi = ( mi , ni , ki ) T (i=1, 2, 3). The force analysis is shown in Fig. 4.

Fig. 4.

¢ , - FBiy ¢ , - FBiz ¢ )T . where Ai Bi = ( mi , ni , ki ) T , FBi¢ = (- FBix

Eq. (13) can be translated into scalar expression as

3.2

T

(13)

1 ì ï ¢ ni + FByi ¢ ki - ml gni = 0, -FBzi ï ï 2 ï ï ï ï 1 í-FBxi ¢ ki + FBzi ¢ mi + ml gmi = 0, i = (1, 2, 3), (14) ï 2 ï ï ï ï ¢ ¢ -F m + FBxi ni = 0. ï ï î Byi i Considering the influence of the local degrees of freedom, Eq. (14) can be expressed as ìï n ¢ = i FBxi ¢ , ïïï FByi m i ï i = (1, 2, 3). í ïï ¢ ki - ml gmi 2 FBxi ¢ = , ïï FBzi 2mi ïïî

(15)

3.3 Static analysis of the sliders in the side limbs The constrained forces of the sliders from the fixed base can be decomposed into two parts, one is the force along the motion direction of the slider, and the other is the force perpendicular to the motion direction of the slider. The force along the motion direction of the slider is the driving force of the shoulder complex mechanism, while the force perpendicular to the motion direction of the slider is only for guiding and has no effect on solving for the driving force from the static equilibrium equations of the mechanism. So the static equilibrium equation of the slider only need to consider the force along the motion direction of the slider to get the driving force denoted as Fmi . The constrain force ¢ , FAiy ¢ , FAiz ¢ )T in from the limb denoted as FAi¢ = ( FAix fixed coordinate system {F}, which is the reacting force of FAi . The force analysis is shown in Fig. 5.

Force analysis of the connecting rod

When the side limbs are in equilibrium state, the force equilibrium equation can be expressed as

FAi + FBi¢ + Gl = 0, i = (1, 2, 3).

(11)

Eq. (11) can be translated into scalar expression as ¢ = 0, ïìï FAxi - FBxi ïï ¢ = 0, i = (1, 2, 3). í FAyi - FByi ïï ïï FAzi - FBzi ¢ - ml g = 0, î

Fig. 5. Force analysis of the sliders

(12)

Choosing the point of Ai to be employed in evaluating the torques, the torque equilibrium equation of the side limbs can be expressed as

When the sliders are in equilibrium state, the force equilibrium equation can be expressed as

¢ ci + FAiy ¢ ci + ( FAiz ¢ + mh g )c i - Fmi = 0, FAix i = (1, 2, 3),

(16)

CHINESE JOURNAL OF MECHANICAL ENGINEERING where

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i —Angle between X axis positive direction and OAi, ci = s ci , i —Angle between Y axis positive direction and OAi, ci = s si ,  i —Angle between Z axis positive direction and OAi, c i = -c . mh —Quality of each slider.

3.4 Static analysis of the middle limb The middle limb connects the moving platform with the spherical pair, and is fixed with the fixed base. So obviously the force exerting on the middle limb by the moving ¢ , - FNy ¢ , platform, which can be denoted as FN¢ = (-FNx -FNz¢ )T in the stationary coordinate system {F}, is equal in size and opposite in direction to the force of FN . ¢ = FNx , FNy ¢ = FNy , and FNz¢ = FNz . Namely FNx From the above mentioned, by solving simultaneous equations composed of Eq. (8), Eq. (10), Eq. (12), Eq. (15) and Eq. (16), a total of 24 forces acting on each component of the shoulder complex mechanism can be calculated with the help of MAPLE software. The analytical solutions of the forces aren’t described in this paper for their great length.

4

Fig. 6.

Relationship between FN¢ and Fz

Numerical Analysis of Static Force on the Shoulder Complex

The structural parameters of 3-PSS/ S shoulder complex mechanism are set as following: L2=48 mm, ε=π/6, l=96 mm, L2=9.6 mm, mo=0.11 kg, ml=0.012 kg, mh=0.023 kg. Substituting the geometric parameters and the external load into the simultaneous equations, then the forces applied on the middle limb and the side limbs can be obtained by calculation with MAPLE software. Considering the limitation of the paper length, parts of the computation results in different conditions are taken as example in the paper. When =–π/6, β=0, γ=0, M=(0 N • m, 0 N • m, 0 N • m)T, Fz changes in the interval of 1 N within the scope of (0 N, 45 N), the varying case of load on the middle limb is shown in Fig. 6. When =–π/6, β=0, γ=0, F=(0 N, 0 N, 2 N)T, Mz changes in the interval of 0.25 N • m within the scope of (0 N • m, 2.75 N • m), the varying case of load on each limb including the middle limb is shown in Fig. 7. From the data in Fig. 6, it can be seen that when the center of the moving platform only suffers a pure force, the force FN¢ has an increasing variation of direct proportion with the load force Fz , while the forces FBi¢ on the side limbs are always 0.015 N and far less than the force on the middle limb. As is shown in Fig. 7, when the moving platform suffers both force and torque, the forces FBi¢ and FN¢ are both varying in direct proportion as the load on the moving platform increasing. And the changing curves of forces on three side limbs are overlapping in this case whose values less than one-tenth of the force FN¢ on the middle limb.

Fig. 7.

Relationship between FN¢ , FBi¢ and M z respectively

When Fw=(5 N, 4 N, 7 N; 0 N • m, 0 N • m, 0 N • m)T, =–π/6 or π/3, β and γ changes separately in an interval of π/30 within the scope of (–π/5, π/5), the value of FN¢ is always 9.747 N, which having nothing to do with the change of the attitude angle. Meanwhile, the constrain force FBi¢ on the side limbs maintain a value at 0.015 N. So the effect of the mechanics unloading of the shoulder complex can be achieved for the middle limb bears load 10 times more than one side limb. When Fw=(0 N, 0 N, 0 N; 3 N • m, 5 N • m, 4 N • m)T, =–π/6 or π/3, β and γ changes separately in an interval of π/30 within the scope of (–π/5, π/5), the relationship between the values of force FN¢ , FB¢1 , FB¢2 , FB¢3 and the attitude angle respectively is obtained as shown in Fig. 8 and Fig. 9. As Fig. 8, Fig. 9 shown, when the pure torque is applied

HOU Yulei, et al: Mechanics Unloading Analysis and Experimentation of a New Type of Parallel Biomimetic Shoulder Complex

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on the moving platform, the value of FN¢ maintains a higher level than the values of FBi¢ . When =–π/6, FN¢ changes within the scope of (1.428 N, 1.856 N), in contrast, the values of FB¢1 ~ FB¢3 are in the scope of (0.201 N, 0.358 N), (0.074 N, 0.140 N) and (0.028 N, 0.304 N) separately, less than 25.07% (the maximum value of FBi¢ /the

minimum value of FN¢ ) of FN¢ . When =π/3, FN¢ changes within the scope of (0.760 N, 1.015 N), the values of FB¢1 ~ FB¢3 are in the scope of (0.039 N, 0.174 N), (0.114 N, 0.240 N) and (0.007 N, 0.098 N) separately, less than 31.58% of FN¢ . That means the middle limb bears quite a meaningful part of external load in this situation.

Fig. 8.

Relationship between FN¢ , FB¢1 , FB¢2 , FB¢3 and the attitude angle respectively when =–π/6

Fig. 9.

Relationship between FN¢ , FB¢1 , FB¢2 , FB¢3 and the attitude angle respectively when =π/3

When Fw=(3 N, 4 N, 5 N; 6 N·m, 4 N·m, 7 N • m)T, =–π/6 or π/3, β and γ changes separately in an interval of π/30 within the scope of (–π/5, π/5), the relationship

between the values of force FN¢ , FB¢1 , FB¢2 , FB¢3 and the attitude angle respectively is obtained as shown in Fig. 10 and Fig. 11.

CHINESE JOURNAL OF MECHANICAL ENGINEERING

Fig. 10.

Relationship between FN¢ , FB¢1 , FB¢2 , FB¢3 and the attitude angle respectively when =–π/6

Fig. 11.

Relationship between FN¢ , FB¢1 , FB¢2 , FB¢3 and the attitude angle respectively when =π/3

As shown in Fig. 10, Fig. 11, the value of FN¢ maintains a higher level than the values of FBi¢ . When =–π/6, FN¢ changes within the scope of (7.542 N, 7.759 N), in contrast, the values of FB¢1 ~ FB¢3 are in the scope of (0.135 N, 0.339 N), (0.121 N, 0.320 N) and (0.007 N, 0.099 N) separately, less than 4.49% of FN¢ . When =π/3, FN¢ changes within the scope of (7.594 N, 7.811 N), while the values of FB¢1 ~ FB¢3 are in the scope of (0.143 N, 0.348 N), (0.129 N, 0.329 N) and (0.002 N, 0.108 N) separately, less than 4.58%

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of FN¢ . From this the middle limbs’ load sharing effect is remarkable. By numerical analysis of the static force on the shoulder complex respectively in pure force, pure torque and composite force load conditions, it can be concluded that the middle limb can bear a considerable proportion of the external load in different working cases, while the side limbs bear a small part of the external load. So the effect of the force unload can be realized. From the other point of

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HOU Yulei, et al: Mechanics Unloading Analysis and Experimentation of a New Type of Parallel Biomimetic Shoulder Complex

view, the mechanical property of the shoulder complex is improved obviously.

5

Force Feedback Experiment of the Shoulder Complex

The prototype mechanism of the shoulder complex consists of two parts: the mechanical body and the electrical control system. The mechanical body mainly comprises the moving platform, the fixed base, limbs with hinges and linear module units etc, as shown in Fig. 12. The electrical control system mainly includes the mechanism movement controller, three SGDV servo units, three servo motors, several displacement transducers and the controller cabinet etc, as shown in Fig. 13.

motor and the force. The force transmission and feedback information of the shoulder complex mechanism can be achieved by comparing the experimental results with the theoretical values of static analysis. As shown in Fig. 14, main devices used for the force feedback experimentation include: the 3PSS/S spherical biomimetic shoulder complex mechanism, one LC1104 micro strain force transducer, one ZP-100 high precision push and pull force transducer, one YASKAWA MP2300S movement controller system, one PH5956D servo units and three servo motors with Hall element en dynamic sign test and analysis instrument, three SGDV coder.

Fig. 14. Experimental system of the shoulder complex

Fig. 12.

Mechanical body of the shoulder complex

Fig. 13. Electrical control system of the shoulder complex

The force feedback experiment is used for describing a mapping relation between the input force and the output force of the biomimetic shoulder complex. A micro strain force transducer is required to be installed on the middle limb. When the force or moment is exerted on the moving platform, the micro strain force transducer on the middle limb would transfer analog output signal to the dynamic signal test and analysis system. Then, the force on the middle limb will be displayed by the system in real time. Meanwhile, YASKAWA movement controller displays the torque output values of the servo motors through analyzing supplying of each motor’s input current from the servo-drive. The force on the side limbs can be calculated by the relational expression between the torque values of the servo

For the convenience of measurement, the incremental force on the moving platform center in the interval of 5 N are exerted by ZP-100 high precision push and pull force transducer when the attitude angle is =–π/6, β=0, γ=0. The peak value of the force on the middle limb is extracted from the dynamic signal test and analysis instrument, while the force on the side limbs is obtained by analyzing the data of movement controller system, as shown in Table 1. When an incremental moment in the interval of 0.5 N • m and a force of 2 N is exerted on the moving platform by the high precision push and pull force transducer, the relational expression between the load on the each limb including the middle limb and the external load is shown in Table 2. What should be explained is that there is a deviation between the theoretical value and the experimental data in Table 1 and Table 2. The possible influence factors include the friction force of the components of the shoulder complex mechanism, the deviation of external load acting point on the moving platform, the selection of measuring methods and the precision of the force cell, etc. From the data in Table 1, it is shown that when the center of the moving platform only suffers a pure external force, the force FN¢ on the middle limb increases as the load on the moving platform increases, while the forces FBi¢ on the side limbs change smoothly and are less than one percent of the force of the middle limb. So it indicates that the middle limb bears the vast majority of the load from the moving platform when the mechanism suffers a pure external force.

CHINESE JOURNAL OF MECHANICAL ENGINEERING Table 1.

Force and torque of each component when the loaded torque is zero Experimental value

Parameter of analysis

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Calculated value

Average absolute

1

2

3

4

5

1

2

3

4

5

error

Loaded force Fx / N

0

0

0

0

0

0

0

0

0

0



Loaded force Fy / N

0

0

0

0

0

0

0

0

0

0



Loaded force Fz / N

5

10

15

20

25

5

10

15

20

25



Loaded torque Mx / (N • m)

0

0

0

0

0

0

0

0

0

0



Loaded torque My / (N • m)

0

0

0

0

0

0

0

0

0

0



Loaded torque Mz / (N • m) Force on middle limb FN¢ / N

0

0

0

0

0

0

0

0

0

0



4.6

9.2

13.9

19.4

23.5

5.31

10.31

15.30

20.31

25.30

0.98

Force on side limb FB¢1 / N

0.019

0.017

0.017

0.018

0.015

0.015

0.015

0.015

0.015

0.015

0.002

Force on side limb FB¢2 / N

0.010

0.010

0.010

0.008

0.005

0.015

0.015

0.015

0.015

0.015

0.006

Force on side limb FB¢3 / N

0.021

0.018

0.018

0.016

0.013

0.015

0.015

0.015

0.015

0.015

0.003

Ratio of torque T1 / %

–0.83

–0.77

–0.77

–0.83

–0.67













Ratio of torque T2 / %

–0.50

0.50

0.50

0.44

0.28













Ratio of torque T3 / %

–0.83

–0.72

–0.72

–0.67

–0.56













Table 2. Parameter of analysis

Force and torque of each component when the loaded torque is not zero Experimental value

Calculated value

Average absolute

1

2

3

4

5

1

2

3

4

5

error

Loaded force Fx / N

0

0

0

0

0

0

0

0

0

0



Loaded force Fy / N

0

0

0

0

0

0

0

0

0

0



Loaded force Fz / N

2

2

2

2

2

2

2

2

2

2



Loaded torque Mx / (N • m)

0

0

0

0

0

0

0

0

0

0



Loaded torque My / (N • m)

0

0

0

0

0

0

0

0

0

0



Loaded torque Mz / (N • m)

0.5

1

1.5

2

2.5

0.5

1

1.5

2

2.5



Force on middle limb FN / N

2.06

2.02

1.99

1.95

1.89

2.34

2.38

2.42

2.46

2.51

0.44

Force on side limb FB¢1 / N

0.049

0.073

0.092

0.120

0.145

0.027

0.065

0.103

0.141

0.179

0.019

Force on side limb FB¢2 / N

0.025

0.041

0.103

0.170

0.227

0.027

0.065

0.103

0.141

0.179

0.021

Force on side limb FB¢3 / N

0.051

0.087

0.123

0.157

0.195

0.027

0.065

0.103

0.141

0.179

0.019

Ratio of torque T1 / %

–2.65

–3.94

–4.97

–6.27

–7.59













Ratio of torque T2 / %

–1.29

–2.03

–5.12

–8.4

–11.30













Ratio of torque T3 / %

–2.72

–4.69

–6.62

–8.43

–10.46













Comment: T1, T2, T3 is the ratio of the driving torque and the rated torque of the motor. The rated torque of the motor is 0.0637 N • m. Average absolute error is the average value of each measuring error between the experimental value and the calculated value.

As is shown in Table 2, when the center of the moving platform suffers a compound force, the forces FBi¢ on the side limbs vary significantly and are less than one-tenth of the force FN¢ on the middle limb as the load on the moving platform increasing. Therefore it indicates that the compound force has a larger influence on forces of the side limbs than a pure external force and the middle limb has an apparent effect of mechanics unloading when the shoulder complex suffers a compound force.

6 Conclusions (1) When the proposed 3-PSS/S spherical parallel shoulder complex mechanism suffers external force or compound force, the middle limb can bear most of the load, while the side limbs bear a small part of the load. (2) The mechanics unloading characteristic of the parallel biomimetic shoulder complex was verified by the static analysis of the mechanism and the force feedback experimentation on the prototype.

(3) The carrying capacity and motion performance of the shoulder complex can be improved by the realization of mechanics unloading of 3-PSS/ S spherical parallel mechanism. References [1] SONG Hongsheng, WANG Dongshu. Research development of bio-robots: a review[J]. Machine Tool and Hydraulics, 2012, 40(13): 179–183. [2] NGUYEN P L, DO V P, LEE B R. Dynamic modeling of a non-uniform flexible tail for a robotic fish[J]. Journal of Bionic Engineering, 2013, 10(2): 201–209. [3] LIU Xinjun, WANG Jinsong, GAO Feng, et al. Design of a serial-parallel 7-DOF redundant anthropomorphic arm[J]. China Mechanical Engineering, 2002, 13(2): 101–105. [4] WANG Xuanyin, ZHANG Yang, FU Xiaojie, et al. Design and kinematic analysis of a novel humanoid robot eye using pneumatic artificial muscles[J]. Journal of Bionic Engineering, 2008, 5(3): 264–270. [5] JUNG Y, BAE J. Kinematic analysis of a 5-DOF upper-limb exoskeleton with a tilted and vertically translating shoulder joint[J]. IEEE/ASME Transactions on Mechatronics, 2015, 20(3): 1428–1439.

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HOU Yulei, et al: Mechanics Unloading Analysis and Experimentation of a New Type of Parallel Biomimetic Shoulder Complex

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Biographical notes HOU Yulei, born in 1980, is currently a professor at Yanshan University, China. His research interests include parallel mechanism, bionics of human robot, nonlinear dynamics, multi-axis force sensor. Tel: +86-13623358151; E-mail: [email protected] LI Zhisen, born in 1988, is currently a master degree candidate at Yanshan University, China. His research interest is parallel mechanism and bionics of human robot. E-mail: [email protected] WANG Yi, born in 1989, is currently a master degree candidate at Yanshan University, China. His research interest is parallel mechanism and its chaotic motion. E-mail: [email protected] ZHANG Wenwen, born in 1981, is currently an experimentalist at Yanshan University, China. His research interests include measuring and testing technique. E-mail: [email protected] ZENG Daxing, born in 1978, is currently an associate professor at Yanshan University, China. His research interests include parallel mechanism, type synthesis, and engineering machinery design. E-mail: [email protected] ZHOU Yulin, born in 1961, is currently a professor at Yanshan University, China. His research interests include bionics of human robot, configuration design of heavy equipment, and electromechanical integration technology. E-mail: [email protected]