A lightweight shoulder prosthesis with antagonistic impact-absorbing hybrid actuation for bimanual activities of daily living

Abstract

In developing a shoulder prosthesis, in addition to appropriate payload and range of motion under the constraints of weight and shape, impact absorption is very important for safe use. Hybridization of two different actuators (pneumatic elastic actuators with the features of lightness and intrinsic visco-elasticity, and servo motors that have stable torque and a large range of motion in combination with an antagonistic mechanism) was employed to achieve the development of the shoulder prosthesis. A two-link, two-degree-of-freedom arm was used to test the different hybridization configurations in order to investigate the impact absorption. A dynamic simulation platform based on four bimanual activities of daily living was established to obtain the required range of motion and torque for joints of a two-link, four-degree-of-freedom arm. The number of pneumatic elastic actuators required and the dimension of the antagonistic mechanism mechanical structures were optimized using the dynamic simulation platform. The best configuration of the two types of actuators was determined using the dynamic simulation based on the impact absorption results and other criteria. Moreover, a simplified prototype driven by hybrid actuation was made. It was shown that the pneumatic elastic actuator joint could improve impact absorption, and the actuator configuration of shoulder prostheses is activity of daily living dependent. The prototype could reproduce a certain activity of daily living motion, indicating its feasibility in daily living.

Keywords

Shoulder prosthesis antagonistic mechanism pneumatic elastic actuator impact absorption activities of daily living

Introduction

Although prosthetic fingers,^1–3 hands,^4–8 trans-radials,^9–11 and other types of prostheses^12,13 have been well studied, there have been few studies on shoulder prostheses. Because shoulder amputees are not able to manipulate their prosthetic arm with a much shorter residual limb, an appropriate output force and range of motion (ROM) are much more necessary than with other prostheses such as hand and trans-radial prosthesis.

In developing a shoulder prosthesis, in addition to appropriate payload and ROM under the constraints of weight and shape, impact absorption is very important for safe use in daily living. However, to the best of our knowledge, there has been no research taking into account these factors, especially safety with validation by testing impact absorption in a comprehensive manner.

Softness of an intact arm could contribute to impact absorption, thus reducing the damage caused by a possible collision with other objects in the course of daily living. Although a motor-actuated mechanism could provide “pseudo-softness” through impedance control with sensory information^14,15 it faces a problem with time delays. On the other hand, flexible components are directly introduced to actuator mechanisms for intrinsic softness. These components were springs, a magnetorheological (MR) damper, shape memory alloys (SMAs), a mechanical prismatic slider, and pneumatic elastic actuators (PEAs).^6,16–24 PEAs are also called pneumatic muscle actuator.^20,22,23 Because the peak value of impact force and acceleration occurs in a very short period of time,^25,26 the intrinsic softness has a beneficial effect over “pseudo-softness” on absorbing the impact from an unpredicted collision. In our previous study, a shoulder prosthesis was designed according to a policy that favored PEAs using a 4-degree-of-freedom (DOF) arm model based on a simplistic straight-line trajectory for a motion of typical activities of daily living (ADLs).²⁷ The impact absorption feature was investigated based on the maximum impact value of a drop impact test with a simplified 1-DOF arm. Apparently, the tests with the 1-DOF arm could not reveal the impact absorption effect of a different combination of actuators.

On the other hand, motors, as actuators, could potentially generate both a large working space and a stable output force. Also, the motion could be controlled to be speedy and accurate. Moreover, motors have advantages of accessibility and cost-effectiveness. In related work of shoulder prostheses, higher DOFs and multifunctional arms driven by motors have been studied.^28–32 The arm²⁹ for targeted muscle reinnervation (TMR) is considered to be an especially state-of-the-art technology. However, such motor devices generally have less back-drivability, due to the strong holding torques and multiple reduction gear. This means that a prosthetic arm and its joints are rigid and could give rise to injuries, because the arm could not cushion the impact of collisions or contacts and consequently convey the impact force to the interface between the prosthesis and the user’s body. Moreover, a motor usually lacks lightness in comparison to its output force. The arm^30,31 taking into account wearability (including usability and comfort) and functionality (from the aspect of payload, velocity, and mobility) incorporates a safety device. The safety device consists of a steel pin and a flat spring, which allows the upper arm to freely rotate in case of an unexpected higher external load acting on the arm in order to prevent the impact force due to accidental impacts from being transmitted to the user’s body. However, with respect to the weight, in turn, many prostheses including the abovementioned shoulder prostheses weigh above 2 kg. However, the lighter weight is desirable for amputees.^33,34

In this study, a hybridization of two different actuators (PEAs and servo motors) in combination with an antagonistic mechanism (AM) was employed to deal with the design problem. PEAs have lightness, intrinsic visco-elasticity (i.e. safety³⁵), and good power-weight performance compared to standard industrial pneumatic cylinder actuators or motors.^36–38 However, they also have a small ROM and a stroke-dependent output force. Moreover, PEAs are slow and inaccurate due to their hysteresis characteristics. The hybridization can take advantage of and compensate for weakness of both the PEA and the motor.³⁹ A two-link, 2-DOF arm was used to test the different configurations of hybridization, in a series of drop impact experiments, in terms of impact absorption. A dynamic simulation platform based on the motion data of four bimanual ADLs including a drinking motion which was measured in our previous study^40,41 was established and used to obtain the required ROM and torque for each joint of the two-link, 4-DOF arm. Because PEAs are prismatic actuators, which could only generate the force by contraction, an AM with a pulley is required in order to generate a bidirectional rotational motion for a joint. The number of PEAs required and the pulley radius in the AM could be optimized using the dynamic simulation platform. Based on the optimization results, the ADL dependency could be investigated. Finally, a prototype could be built and used for investigating the reproducibility of a certain ADL.

Methods

Drop impact test

In order to compare the impact absorbability between the PEA AM and the servo motor joint in a multiple joint situation, drop impact tests were performed on a two-link, 2-DOF arm, which consists of two links, L_U (upper arm link) and L_F (forearm link), and two joints, J_S (shoulder joint) and J_E (elbow joint). J_S was linked to a sliding table with a rotational shaft and ball bearings. The sliding table was placed on the measurement plane of the sensor of the force gauge (ZTA-DPU-500N, IMADA Corp., 2000 Hz, 500 N).⁴² J_S and J_E were connected to and actuated through the output rotational shaft of the PEAs (PM-10P, SQUSE Inc., Japan, 0.003 kg, 23.8 cm³ (simulated value), maximum 100 N, average contraction ratio 30% per piece)⁴³ or the motor (RS405CB, Futaba Corp., 0.067 kg, 35.6 cm³, 4.7 N m (48.0 kg cm, gravity acceleration g = 9.8 m/s²))⁴⁴ as shown in Figure 1(a)–(c).

Figure 1.

Test arm of two-link-2-DOF: (a) experimental equipment of impact force measurement. The test arm consists of the link L_U (upper arm) and L_F (forearm) with joint J_S (shoulder) and J_E (elbow). (b) AM with four PEAs and a pulley of radius r = 30 mm. Its output rotational shaft is connected to J_S or J_E. (c) Servomotor whose output rotational shaft is connected to J_S or J_E. (d) Configuration SM-EM in Table 1. The motor in (c) is connected to J_S and J_E. (e) SP-EM. The AM with four PEAs (b) and motor is connected to J_S and J_E, respectively. (f) SM-EP. The motor and AM with four PEAs are connected to J_S and J_E, respectively. (g) SP-EP. The AM with four PEAs is connected to J_S and J_E.

Four configurations, shown in Table 1 and Figure 1(d)–(g), were tested. In fact, the PEA joint can generate the torque by composing the AM as shown in Figure 1(b). In our previous experiments, the relationship between the stroke x_PEA (mm) and output force F_PEA (N) of the PEA for air pressures of 0.2 MPa was derived as follows.²⁷ In the experiments,²⁷ three pieces of PEAs, which were connected serially, were used for averaging purposes. Weights from 1 kg (9.8 N) to 10 kg (98 N) were added in increments of 1 kg (9.8 N) to the end of the series of PEAs, and 0.2 MPa air pressure was applied (all PEAs were actuated) after adding each weight. The change in length, x_PEA, with respect to the unloaded natural length of each PEA piece was measured under each weight, and the measurements were repeated 10 times. The relationship, which was considered to be linear, was shown in the measurement region (9.8–98 N)

F_{PEA} = - 4.61 x_{PEA} + 98.02

(1)

Table 1.

Impact test configurations.

Configuration	Joint
Configuration	Shoulder	Elbow
1. SM-EM	Motor	Motor
2. SP-EM	PEAs	Motor
3. SM-EP	Motor	PEAs
4. SP-EP	PEAs	PEAs

PEA: pneumatic elastic actuator; SM-EP: shoulder-motor-elbow-PEA; SM-EM: shoulder-motor-elbow-motor; SP-EM: shoulder-PEA-elbow-motor; SP-EP: shoulder-PEA-elbow-PEA.

Two PEAs were used in parallel on each side as shown in Figure 1(b) (a total of four PEAs), and their lengths were adjusted while considering equation (1), and the radius, r, of the pulley was set to 30 mm in order to compare the PEAs and AM joint with the motor joint under similar conditions.

Weights of 0.98 and 1.96 N were dropped from a height of 30 mm and collided with a cover which was fixed on the L_F for avoiding a collision with the PEAs, as shown in Figure 1(a), (f), and (g). When using the PEAs and AM, air pressures of 0.2 and 0.1 MPa were tested. The following are indexes measured in the test. All measurements in the collision experiments were repeated 10 times for averaging purposes. Here, the undernoted average impact difference value represented roughly the vibrational transmission and was measured every 0.0005 s for 0.4 s (800 points) after the collision as shown in Figure 2.

Waveform for 0.5 s (1000 measured points);

First peak of impact force;

Second peak of impact force;

Time from collision to second peak;

Average of impact difference value (Id) for 0.4 s.

Figure 2.

Average impact difference value. The average impact difference value per 0.0005 s in waveform for 0.4 s was measured. Moreover, this value was also averaged by 10 repetitions.

ADL measurement

In order to accomplish the goals of the shoulder prosthesis, which is lightweight, simple, and useful for matching the needs of users, the prosthetic mechanism should be designed with a focus on the motion or functions of intended ADLs. This focus leads to an improvement of lightness and simplicity, that is, maintenance and lasting usage.^45,46 Unilateral arm amputees are deemed capable of carrying out roughly 80% of ADLs with their intact arm.⁴⁷ Therefore, prostheses with functions that support bimanual coordination motions are considered reasonable except for one-handed ADLs. In this article, four such bimanual ADLs were selected as intended motions for development of the prosthesis as follows. The motions were conducted by one healthy subject, who was 170.5 cm tall and right-handed. The left-hand coordinate was measured by a motion tracking system (OptiTrack, 60 Hz) and is depicted as red plots in Figure 3. The position of each part was laid out as shown in Figure 3.

Drinking: reaching for, grasping, unscrewing the top of (by the right hand), and drinking a bottled water of 0.5 kg in a sitting posture;

Putting on socks of 0.05 kg in a sitting posture;

Tying: wearing a tie of 0.05 kg in a standing posture;

Hanging; hanging up a washed cloth (shorts 0.2 kg) using clothespins in a standing posture.

Figure 3.

Motions of four ADLs: (a) reaching for, grasping, unscrewing the top of, and drinking bottled water in a sitting posture; (b) putting on socks in a sitting posture; (c) wearing a tie in a standing posture; and (d) hanging up a washed cloth (shorts) using clothespins in a standing posture.

Link model simulation

In order to calculate the required joint ROM and torque when conducting the four ADL motions, a shoulder prosthesis link model for a prototype was developed as shown in Figure 4. The model consisted of two links (upper arm, L_UA, and forearm with hand, L_FAH), two joints (2-DOF shoulder J₁–J₂ and 2-DOF elbow J₃–J₄), and a 1-DOF hand whose ROM and torque were not calculated, and only one dimension was used as a part of L_FAH in the link model simulation. The prototype based on the model aims to reproduce the ADL motion. In this study, it was assumed that the prosthesis prototype would not be applied to amputees directly but rather to healthy subjects first to confirm the validity of the design and its performance. Thus, the model generating the prototype was designed to be worn at the front of the intact shoulder of the healthy subject who conducted the four ADL motions in the previous section using a socket, as shown Figure 4(b) and (c). Body surface data of the subject in Figure 4(b) were scanned by a three-dimensional (3D) scanner, and the socket fitting the shoulder and fixing the link was designed. A global coordinate system O -XYZ was fixed at the left acromion shown as Figure 4(b) and (c). Let the intersection point of J₁ and J₂ in the O -XYZ, the angle of the joint J (J₁, J₂, J₃, J₄), the length of Link L(L_UA, L_FAH), and the coordinate of the hand position (i.e. trajectory) be O_J _1J2 , θ (θ₁, θ₂, θ₃, θ₄), l (l_UA, l_FAH), and P (x, y, z), respectively. Then, P could be taken as functions of the l and θ as equation (2). Moreover, in order to examine the required torque T (T₁, T₂, T₃, T₄) of the joint J , the dynamical equation was derived as equation (3).⁴⁸ The θ was calculated by substituting the trajectory in Figure 3 into the P in equation (2) using a numerical solution, and T was derived by substituting θ into equation (3). The link model was offset 135 mm from the intact arm in the Y-direction for installing the prototype at the intact shoulder as shown in Figure 4(d). Therefore, in fact, the start and end part of the raw trajectory data measured in all the ADL motions were partially offset and modified alike as blue plots shown in Figure 4(e). Moreover, these trajectory data were smoothed using a moving average of 10 points and three repetitions for the dynamical calculation. A constraint condition was set up so that the axis A_HY at hand in the O -XYZ in Figure 4(b) was always in the sagittal plane (the Y–Z plane with an arbitrary X position). This allows the hand to grasp an object, such as a drinking cup on a table, easily. The motion of the link was simulated under these conditions. The link length was decided based on the arm length from the scanned data, and the weight was set as shown in Figure 4(c). The load at the hand, Fz, was assumed to change depending on the type of ADL as shown in Figure 4(c) and as described in previous section.

P = {O_{J}}_{1 J 2} + f (l, θ)

(2)

T = H (θ) \overset{\cdot\cdot}{θ} + C (θ, \overset{\cdot}{θ}) + G_{f} (θ) g + J_{f}^{T} (F, N)

(3)

where H(θ) is the inertia term, $C (θ, \overset{\cdot}{θ})$ is the Coriolis term, G_f(θ) is the gravity term, $J_{f}^{T} (F, N)$ is the external force term including transposed Jacobian matrix, (F, N) is the external force F(F_x, F_y, F_z), and moment N(N_x, N_y, N_z) acting on P.

Figure 4.

Link model. (a) Two-link, 4-DOF link arm model. (b) Global coordinate system O -XYZ at the left acromion, 3D data of body surface and socket, and axis A_HY at hand. (c) Length, weight of two links, load at hand and joint rotational direction in O -XYZ. (d) Link model offset 135 mm from the intact arm in Y-direction. (e) Pathway (blue) whose start part was offset 135 mm from raw measured trajectory (red) in Y-direction. (f) Yellow plots are the chosen six points for the prototype motion (described in section “Results”).

AM optimization

In order to compose the AM using PEAs for joints of a two-link, 4-DOF prosthesis, several factors need to be determined. In this study, the required number of the PEAs and the radius of a pulley in the AM were used as parameters for the optimization. Multiple PEAs were applied in parallel and in series depending on the required joint ROM and torque calculated for ADL motions using equation (3) as shown in Figure 5. Then, let the number of PEA serial and parallel connections, the pulley radius, and the torque generated by the AM in the joint J be sc (sc₁, sc₂, sc₃, sc₄), pc (pc₁, pc₂, pc₃, pc₄), r _AM (r_AM1, r_AM2, r_AM3, r_AM4), and T _AM (T_AM1, T_AM2, T_AM3, T_AM4), respectively. This relationship was derived by substituting the joint angle θ (in degrees) which was derived from equation (2) into equation (4).²⁷ This equation (4) was used not only for the AM in the joint of the prosthesis link model, but also for the AM of the 2-DOF test arm used in the drop impact experiments as shown in Figure 1. When an exploration on all parameters was conducted, the parameters sc , pc , and r _AM are changed as in equation (5). A total of 46 × 9 = 414 combinations could be made for all joints in all ADL motions. For selecting prospective solutions from the combinations, thresholds were set as shown in equation (6).

Figure 5.

AM composed by PEAs: (a) case of one PEA on the antagonist side and one PEA on the agonist side. Thus, total PEAs are 2 (sc = 1, pc = 1); (b) four PEAs on each side (sc = 2, pc = 2); and (c) six PEAs on each side (sc = 2, pc = 3).

Considering the sampling rate of the motion tracking system for ADL measurement, the point data of P were measured every 1/60 s. Thus, the combinations of which the minimum of 100 × ( T _AM − T )/ T for all points was more than 10% in each ADLs trajectory were selected as candidates. This criterion requires that the torque generated by AM with PEAs have enough margin of power to drive the joint. Here, comparing J₄ − L_FAH in Figure 4(c) to the output rotational shaft framework in Figure 5, the axis direction of the joint rotation against the link differs by 90° in the relationship. Therefore, a drive box for the bevel gear was employed when the L_FAH shown in Figure 4(c) was assumed to be the framework in Figure 5(a). The weight of the bevel gear was calculated in the after-mentioned simulations.

\begin{matrix} T_{AM} = F_{PEA} r_{AM} = pc (\frac{- 4.61 x_{PEA}}{sc} + 98.02) r_{AM} \\ = pc (- 4.61 \frac{2 π r_{AM} θ / 360}{sc} + 98.02) r_{AM} \end{matrix}

(4)

\begin{matrix} sc = 1, 2, \dots, 10, pc = 1, 2, \dots, 10, sc \times pc \leq 20, \\ r_{AM} = 10, 15, 20, 25, 30, 35, 40, 45, 50 (mm) \end{matrix}

(5)

100 \times (\frac{T_{AM} - T}{T}) \geq 10 (%)

(6)

where T_AM is the torque generated by the AM in joint J and T is the required torque of J.

Finally, the optimal parameters were decided with the following estimative indexes of the candidates. To keep the balance, for example, it was setup such that a solution with sc = 4, pc = 5 had a higher preference over the solution with sc = 2, pc = 10, although both solutions needed 20 pieces of PEAs. In all the indexes, the minimum number of pieces of PEAs had the highest priority.

Minimum number of pieces of PEAs;

Maximum ROM;

Larger margin (100 × ( T _AM − T )/T);

Balance between sc and pc .

Optimization of hybrid actuation: selection strategy of actuators in joints

Taking into consideration the results of the drop impact test and the required number of pieces of PEAs, that is, the weight of the AM with the PEAs including the pulley and accessory, a decision was made in each joint about whether the AM configured in the previous section was employed using the dynamic simulation platform. If the AM was calculated to be unfit for a certain joint because of such a consideration, the motor was used in place of the AM for the joint. In this article, to select the weight of the AM, 0.067 kg, which equaled the weight of one motor, was set as a single criterion for the judgment. In this way, the two-link, 4-DOF prosthetic arm model was configured. As a result, whether an ADL-independent configuration could be acquired could be investigated.

Reproducing of ADL motion with prototype

Based on the configurations acquired using the dynamic simulation platform, a prototype was built and tested for a trajectory reproducing the experiment in order to explore its feasibility in daily living.

Results

Drop impact test

The results of the evaluation indexes described in subsection “Drop impact test” of section “Methods” are shown in Figures 6 and 7. The waveform was made using the average values for 10 times of measurement. In the waveform shown in Figure 6, the data were smoothed using a moving average of 10 points and three repetitions for visibility. Here, measured negative values, which meant a tensile force, were due to the effect of load cell inertia in the force gauge. The average values of raw data were used in Figure 7 too.

Figure 6.

Waveform for 0.5 s after collision: (a) test under a condition that the collided weight = 0.98 N and air pressure of PEAs = 0.1 MPa; (b) 0.98 N and 0.2 MPa; (c) 1.96 N and 0.1 MPa; and (d) 1.96 N and 0.2 MPa.

Figure 7.

Evaluation indexes in impact test: (a) first peak of impact force for 0.5 s, (b) second peak of impact force for 0.5 s, (c) time from collision to second peak, and (d) average impact difference value for 0.4 s.

Link model simulation and AM optimization

The results of the simulation for four ADL motions are shown in Figure 8 and Table 2. The required joint angle θ , torque T , enable torque, T _AM , and required number of PEAs in each AM were calculated with the link model superimposed with the trajectory of the four ADLs. In Table 2, the number of required PEAs is the sum of both the antagonist and agonist sides in Figure 5. The initial posture of the AM joints could be setup to meet different rotation requirements: bidirectional rotation which means that the θ in Table 2 ranges from a negative angle to a positive angle or a unidirectional rotation which means that the θ does not change its sign. In Figure 8, the absolute values of T _AM and T are used to make clear the relation between T _AM and T . As the results show, for the AM with PEAs of the J₂ in the hanging motion, parameters could not be chosen to meet the constraint condition in equations (5) and (6). The best result within the failure combinations, that is, pc₂ = 4, sc₂ = 5, and r _AM = 25 mm was shown as a guide in Figure 8(d) and Table 2. In Figure 8(d)-J₂, T_AM2 falls well below T₂ about 1.2 sec later. Therefore, J₂ in the hanging motion has to use the motor. The configuration of two types of actuators for the arm in the remaining joints in four ADLs is described in the next section. For all four ADL motions, vibration occurred in T_AM1 and T_AM4, which resulted from a rapidly switched activation of antagonist and agonist.

Figure 8.

Required joint angle θ, torque T, and enabled torque T_AM of AM with PEAs: (a) θ, T, and T_AM in drinking motion; (b) motion of putting on socks; (c) tying motion; and (d) hanging motion. Due to the failure combination, T_AM2 falls well below T₂ in J₂.

Table 2.

Configurations for AM with PEAs in four ADL motions.

	Joint	Number of required PEAs	Combination		r_AM (mm)	Required θ (°)		Absolute max θ of AM	Absolute max required T	Total PEAs		Pulley		Accessory (kg)	Total		100 × (T_AM − T)/T
	Joint	Number of required PEAs	pc	sc	r_AM (mm)	Min	Max	(°)	(N m)	Weight (kg)	Volume (cm³)	Weight (kg)	Volume (cm³)	Accessory (kg)	Weight (kg)	Volume (cm³)	100 × (T_AM − T)/T
Drinking	J₁	2	1	1	10	−44.2	12.0	60.9	0.133	0.006	47.5	0.01	7.5	0.01	0.026	55.0	317.7
	J₂	12	2	3	35	1.6	49.8	104.4	3.990	0.036	285.0	0.03	23.0	0.06	0.128	308.0	14.6
	J₃	18	3	3	15	51.0	114.3	243.6	2.458	0.054	427.5	0.01	9.2	0.09	0.157	436.7	14.3
	J₄	2	1	1	10	−43.1	3.0	60.9	0.001	0.006	47.5	0.01	7.5	0.036	0.052	55.0	64776.7
Putting on socks	J₁	2	1	1	10	0.1	34.9	121.8	0.051	0.006	47.5	0.01	7.5	0.01	0.026	55.0	115.8
	J₂	4	2	1	15	−18.5	5.8	40.6	1.182	0.012	95.0	0.01	9.2	0.02	0.045	104.2	12.0
	J₃	8	2	2	10	39.9	86.8	243.6	1.037	0.024	190.0	0.01	7.5	0.04	0.074	197.5	28.6
	J₄	2	1	1	10	−27.0	−0.1	121.8	0.001	0.006	47.5	0.01	7.5	0.036	0.052	55.0	2755.4
Tying	J₁	4	1	2	10	−61.8	54.8	121.8	0.179	0.012	95.0	0.01	7.5	0.02	0.042	102.5	189.6
	J₂	4	1	2	10	−57.8	−18.7	243.6	0.697	0.012	95.0	0.01	7.5	0.02	0.042	102.5	13.1
	J₃	12	2	3	10	50.5	154.0	365.5	0.994	0.036	285.0	0.01	7.5	0.06	0.106	292.5	20.0
	J₄	2	1	1	10	−48.8	20.2	60.9	0.002	0.006	47.5	0.01	7.5	0.036	0.052	55.0	24296.9
Hanging	J₁	2	1	1	10	−35.1	1.4	60.9	0.184	0.006	47.5	0.01	7.5	0.01	0.026	55.0	197.4
	J₂	40	4	5	25	−12.9	106.6	121.8	3.306	0.120	950.0	0.02	14.7	0.2	0.340	964.7	−
	J₃	12	3	2	10	23.2	112.0	243.6	1.502	0.036	285.0	0.01	7.5	0.06	0.106	292.5	16.6
	J₄	2	1	1	10	−25.6	2.9	60.9	0.001	0.006	47.5	0.01	7.5	0.036	0.052	55.0	49831.7
									Max output torque (N m)
Motor								300	4.70						0.067	35.6

AM: antagonistic mechanism; PEA: pneumatic elastic actuator; ADL: activity of daily living.

Optimization of hybrid actuation: consideration of actuator configuration

The configuration of two types of actuators for the arm was decided based on the results of the drop impact test and simulation. At first, essentially, the shoulder-PEA-elbow-PEA (SP-EP), shoulder-PEA-elbow-motor (SP-EM), and shoulder-motor-elbow-PEA (SM-EP) showed better impact absorption than shoulder-motor-elbow-motor (SM-EM) under all conditions of air pressure and weight of collision, as shown in Figures 6 and 7. Moreover, in comparison between SP-EM and SM-EP, SM-EP was considered to have better absorption because of smaller peak values, longer time to peak, and smaller average impact difference, which means lower vibration. Therefore, it is clear that the AM with PEAs in the elbow is effective. However, this is considered to be because of the collision point on the forearm link, L_F, was closer to the AM in the elbow. Therefore, the impact to the shoulder was decreased. For achieving softness of the two-link, 4-DOF arm as a whole, either shoulder, J₂, or elbow, J₃, should employ the AM against a disturbance in the direction of gravitational force, as shown in Figure 4(c) and the drop impact test results.

On the other hand, the simulation results revealed the disadvantages of the AM. First, the number of PEAs in the AM for each ADL motion was various. The AM of J₂ could not meet the requirement in the hanging motion as described in previous section. On another front, a lot of PEAs were required in J₃ for the elbow; more than J₂ in the remaining three motions. Above all, the AM of J₃ in the drinking motion was heavier than the weight of two motors, 0.134 kg. Therefore, considering the difference of results between the impact absorption and the weight between the AM and motor, the motor was considered to be realistically suitable for J₂ in the hanging motion and for J₃ in the drinking motions.

Second, J₁ and J₄ did not require a large torque and ROM, that is, a lot of PEAs. Comparing the AM with one motor with respect to weight and volume, there is not much difference between the two types of actuators relative to the situation of J₂ and J₃ as shown in Table 2. Therefore, the PEAs with an AM were also employed in J₁ and J₄, in all ADL motions. The above results in the actuator configuration for each ADL motion were rounded up in Table 3.

Table 3.

Actuator configuration of the arm for each ADL.

ADL	J₁	J₂	J₃	J₄
Drinking	PEA	PEA	Motor	PEA
Putting on socks	PEA	PEA	PEA	PEA
Tying	PEA	PEA	PEA	PEA
Hanging	PEA	Motor	PEA	PEA

PEA: pneumatic elastic actuator; ADL: activity of daily living.

Reproducing of ADL motion with prototype

Based on the configurations in Table 3, a prototype was built and used for a trajectory reproducing the experiment in order to explore its feasibility in daily living. In this article, the objective motion for the reproduction was set to the drinking motion, and adapting all ADL motions is a future objective. Moreover, in all ADLs, including the drinking motion in Figure 8, the rotational direction change that is, on-and-off of the activation for the PEAs in J₁ and J₄ was often repeated every minute in the simulation. The PEAs are considered to be difficult to control for such behavior due to their hysteresis characteristics and low reaction speed. Moreover, J₁ and J₄ are insulated from the influence of gravity, that is, the weight of a collision object comparing J₂ and J₃. Therefore, in this article, we give priority to validating the feasibility of a lightweight shoulder prosthetic arm with hybrid actuation, a simplified prototype where the AM with PEAs was changed to the motor in J₁ and J₄ as shown in Table 4. Prototyping, which fully follows the configuration in Table 3, and building the control aspect adaptive to the configuration will be addressed in another paper.

Table 4.

Actuator configuration for the simplified prototype for drinking motion.

ADL	J₁	J₂	J₃	J₄
Drinking	Motor	PEA	Motor	Motor

ADL: activity of daily living.

The prototype was designed and built as shown in Figures 9 and 10. The body surface data of the subject were used for a decision of the dimension and shape of the prototype including the two-link, 4-DOF arm, shoulder socket fitting the subject’s shoulder, and 1-DOF hand performing bottle grasping. The hand was specialized for grasping a bottle for simplicity and lightness using the data as shown in Figure 9(a). The motor of J₃ was placed at a proximal part in the upper arm for decreasing its weight’s influence on the J₂, and it drove J₃ with a belt pulley as shown in Figure 9(b). The whole weight of the prototype arm including actuators was 0.776 kg, as shown in Figure 10(a). In this article, a backpack system, which could decrease the fatigue of user’s lower back by transferring the weight of the distal arm to the proximal trunk, was employed,⁴⁹ and the 12 PEAs of J₂ and the servo motor which was employed for J₅ was set in the backpack using remote actuations with flexible Bowden cables as shown in Figure 10. By transferring the PEAs for AM to the backpack, the space for the installation could be ensured, and multiple actuators could be embedded by connecting them with pc and sc . The hand grasping power simulated and in an experimental result was 124.3 and 61.9 N, respectively. The hand could grasp a bottled water of 0.5 kg in the experiment.

Figure 9.

Design of prototype. (a) 3D model of socket and 1-DOF hand. The hand was designed to generate a grasping force of more than 100 N, and only the thumb was set to rotate around J₅. (b) Prototype of shoulder prosthesis. The prototype was offset 135 mm from the intact arm in the Y-direction as described in subsection “Link model simulation” of section “Methods.”

Figure 10.

Prototype worn by subject: (a) the weight of the hand, forearm, upper arm, socket, and backpack was 0.102, 0.158, 0.516, 0.244, and 0.924 kg, respectively; (b) lateral view of prototype; and (c) back view of prototype.

In the AM of J₂, an open-loop proportional controller was used to regulate the air pressure for PEAs, and gain desired θ₂. Although the blue pathway made by modifying the hand tracking data in Figure 4(e) was used to calculate the θ of joints in the prototype arm as described in subsection “Link model simulation” of section “Methods,” six feature points in P were chosen from the pathway and recalculated to control each joint angle for simplicity of the execution of the drinking motion, as shown in Figure 4(f), and the prototype was set to move to pass through the six points.

The results of the experiment are shown in Figure 11. An error between the hand position in the trajectory and the six points of the target was caused by the influence of a minor deviation of the subject’s posture and a slippage of the socket when reproducing the drinking motion, as observed in Figure 11. Thus, the hand and mouth position were required to change slightly with the trunk and neck motions of the subject for grasping at point 5 and the drinking at point 6 in order to ensure the execution of the ADL motion. Finally, the prototype could move the grasped bottled water of 0.25 kg (including the weight of the motion tracking marker that was mounted at the upper part of the bottle) to the mouth.

Figure 11.

Experiment of drinking motion: (a) Point 1 (start point) in the motion in Figure 4(f); (b) Point 2 (reaching); (c) Point 3 (reaching); (d) Point 4 (reaching); (e) Point 5 (grasping and unscrewing the top); (f) Point 6 (drinking); and (g) measured trajectory of intact hand, of prototype, and the six target points. Errors between points 1–6 and the trajectory at each point are 43.6, 58.0, 37.2, 19.2, 59.8, and 74.5 mm, respectively.

Discussion

At first, the joint with PEAs showed the best validity with respect to impact absorption. SP-EP showed not only smaller first and second peak values and a longer time from collision to the second peak, but also smooth and low-vibration waveforms in Figures 6 and 7. This slow transmission of the force provides a possibility for additional development, for instance, reaction with some control strategy. In general, SM-EP showed better index values than SP-EM. This is because that collision point is closer to the AM joint with PEAs in SM-EP combination, as described in subsection “Optimization of hybrid actuation: consideration of actuator configuration” of section “Results.” Therefore, AM should be used in either a shoulder or elbow to guarantee preferential softness.

In the simulation, the decided configurations of PEAs in the AM of each joint for each ADL motion, that is, ROM and torque, were not same. Moreover, the layout of PEAs and AM/motor for each joint in the arm was also different between all ADLs. At first, the hanging trajectory was different from the other three motions in terms of more distance and a higher reaching motion as shown in Figure 3. This means needing a larger angle of the shoulder, J₂, for the hanging motion. Moreover, an AM with PEAs joint that meets the condition in equations (5) and (6) could not be acquired. That means more than 40 PEAs will be necessary, which is impractical. Therefore, the AM joint was confirmed to be inappropriate for such motion because the joint angle, that is, the PEAs contraction is larger, and output is smaller as shown in equation (1). Therefore, too many PEAs were necessary. In other words, the AM shoulder joint is considered to be suitable for a working space that was lower than around the mouth from the results of drinking, tying, and putting on socks.

In the drinking motion, the shoulder J₂ was small, and the elbow J₃ was large, contrary to the hanging motion. This is just as valid for the motions of putting on socks and tying because subjects move their hand close to their body by folding their arm, that is, elbow, for the motion at the space close to the body. Therefore, the motor was employed for J₃ in drinking. The unnecessity of the motor, that is, fewer PEAs in the AM for J₃ in putting on socks and tying than drinking in spite of a larger angle is considered to be due to the lighter weight of 0.05 kg compared to 0.5 kg for the drinking bottle as described in subsection “ADL measurement” of section “Methods.” Moreover, the actuator configuration of the arm, which enables it to perform all four ADL motions simultaneously, is shown in Table 5. Basically, the greater the number of ADL motions that are intended, the more PEAs, and the bigger the total weight (kg) and volume (cm³) that is required in order to cover various joint angles, rotational directions, and torques. Hence, the motor application increases for the conformance to many ADL motions. However, in case of a similar joint angle and torque, such as the relationship between the tying motion and the putting on socks motion, the same actuator configurations are employed, as shown in Table 3. Therefore, factors such as the number of intended ADLs influencing the necessary joint angle and torque, the similarity or multiplicity between intended ADLs, and the PEA joint’s adoption, that is, prioritizing safety and softness, are considered to be in a trade-off relationship.

Table 5.

Actuator configuration for all four motions.

ADL	J₁	J₂	J₃	J₄
All four motions	Motor	PEA	PEA	Motor

ADL: activity of daily living.

In all four ADLs, the load of J₁ and J₄ was lighter. This is considered to be due to immunity from the gravity force directly. Therefore, the PEAs with an AM were employed for J₁ and J₄ in the simulation, although the motor was used in the prototype. The difficulty of controlling PEAs with their hysteresis characteristics and low reaction speed was considered, and the vibration that occurred in J₁ and J₄, which resulted from rapidly switched activation of antagonist and agonist, is shown in Figure 8. In the future, the influence of the hysteresis using PEAs with an AM joint in J₁ and J₄ with the real machine must be investigated.

Next, the prototype two-link, 4-DOF arm with a 1-DOF hand is discussed. The weight, 0.776 kg, of this prototype arm (compressor, battery, and control unit were not included) was considered to be light in comparison to the other prosthetic arms^13,28,30,32 as shown in Table 6. Moreover, because the forearm and hand had a sufficient strength for the drinking motion, it is possible to reduce the weight additionally by decreasing the thickness of the ribs in the chassis. The grasping force was approximately half of the simulated value as described previously. This is considered to be due to the cable routing and wire stretching and should be remedied in future. The hand itself could grasp the bottle of 0.5 kg. However, the arm could not convey the bottle of 0.3 kg in the experiment of drinking motion. This was influenced by a belt slippage of the joint J₃ in Figure 9(b). Therefore, an improvement of the transfer mechanism could enhance the performance. The anthropomorphic hand and forearm appearance were materialized with the 3D scanner and designed so that the socket could fit the shoulder of the healthy subject. However, the deviation of the subject’s trunk posture and shoulder socket caused the trajectory error shown in Figure 11(g). A minor gap between the socket and the intact shoulder was considered to have an effect on the hand trajectory. It is necessary to improve the fixation of the socket. In the future, a meaningful challenge for the trajectory generation is to implement a method of the feedback control that can improve the precision.

Table 6.

Comparison of weight.

Developed prosthetic arm	DOF		Total weight (kg)
Developed prosthetic arm	Arm	Hand	Total weight (kg)
Arm from hand to above elbow¹³	4	1	2.3
Arm from hand to shoulder²⁸	7	6	3.885
Arm from hand to shoulder³⁰	5 (including passive 1-DOF)	unknown	2.65(accurately CAD model value)
Arm (Gen 3 SC Arm) from hand to shoulder³²	6	4 (with additional passive DOF)	4.45
Our arm from hand to shoulder	4	1	0.776 (without socket)

DOF: degree of freedom; CAD: computer-aided design.

Conclusion

In this article, hybridization of two different actuators, PEAs and servomotors, in combination with an AM, was employed to deal with the design problem of shoulder prostheses. A two-link, 2-DOF arm was used to test the different configuration of hybridization in a series of drop impact experiments, in terms of impact absorption. A dynamic simulation platform based on the motion data of four bimanual ADLs was established and used to obtain the required ROM and torque for each joint of the two-link, 4-DOF arm. The number of PEAs required and the dimensions of the mechanical structures for the AM were optimized using the dynamical simulation platform. According to the experiment and based on the drop impact test results and other criteria, the configuration of two types of actuators was determined, and a simplified prototype was made.

Results showed that the joints with PEAs could absorb more impact force than with motors. The ADL measurement experiments revealed that the actuator configuration of shoulder prostheses is ADL dependent. In motions requiring more distance and higher reach, such as the hanging motion, a larger angle and torque of the shoulder, J₂, were necessary. Therefore, the PEAs with an AM joint were confirmed to be inappropriate for such motion. Consequently, the motor joint predominated the candidate pool, more than the PEAs, which needed a considerable number of pieces. The AM with PEAs is suitable for the motions that do not require high and distant reaching. Based on these results, a simplified shoulder prosthesis that met the ROM and torque requirements for one specific ADL was prototyped, and the trajectory of the ADL was reproduced. The prototype with the hybridization of two different actuators could reproduce the ADL motion, indicating its feasibility in daily living.

However, it is necessary to conduct further investigation. The prototype, which fully follows the optimized configuration, as shown in Tables 3 and 5, that is, the compatibility for other important ADLs motions and control for the visco-elasticity and the motion with hysteresis of PEAs, should be addressed in future.

Footnotes

Appendix 1

Academic Editor: Alicia Casals

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was primarily supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (B), Grant Number 26282160.

References

Low

Kasim

MAA

Koch

. Hybrid-actuated finger prosthesis with tactile sensing. Int J Adv Robot Syst 2013; 10: 351.

Tarvainen

TVJ

Gonzalez

. Development of MorphHand: design of an underactuated anthropomorphic rubber finger for a prosthetic hand using compliant joints. In: Proceedings of the 2012 IEEE international conference on robotics and biomimetics (ROBIO 2012), Guangzhou, China, 11–14 December 2012, pp.142–147. New York: IEEE.

Bandara

DSV

Gopura

RARC

Kajanthan

. An under-actuated mechanism for a robotic finger. In: Proceedings of the 4th annual IEEE international conference on cyber technology in automation, control, and intelligent systems (CYBER), Hong Kong, 4–7 June 2014, pp.407–412. New York: IEEE.

Andrianesis

Tzes

. Design of an anthropomorphic prosthetic hand driven by shape memory alloy actuators. In: Proceedings of the 2nd biennial IEEE/RAS-EMBS international conference on biomedical robotics and biomechatronics, Scottsdale, AZ, 19–22 October 2008, pp.517–522. New York: IEEE.

Scott

Perez-Gracia

. Design of a prosthetic hand with remote actuation. In: Proceedings of the 34th annual international conference of the IEEE Engineering in Medicine and Biology Society (EMBC’12), San Diego, CA, 28 August–1 September 2012, pp.3056–3060. New York: IEEE.

Kaplanoglu

Design of shape memory alloy-based and tendon-driven actuated fingers towards a hybrid anthropomorphic prosthetic hand. Int J Adv Robot Syst 2012; 9: 77.

Polisiero

Bifulco

Liccardo

. Design and assessment of a low-cost, electromyographically controlled, prosthetic hand. Med Dev Evid Res 2013; 6: 97–104.

Gonzalez

Soma

Sekine

. Psycho-physiological assessment of a prosthetic hand sensory feedback system based on an auditory display: a preliminary study. J NeuroEng Rehabil 2012; 9: 33.

O’Neill

An advanced, low cost prosthetic arm. In: Proceedings of IEEE sensors, Valencia, 2–5 November 2014, pp.494–498. New York: IEEE.

10.

Bandara

DSV

Gopura

RARC

Hemapala

KTMU

. A multi-DoF anthropomorphic transradial prosthetic arm. In: Proceedings of the 2014 5th IEEE RAS & EMBS international conference on biomedical robotics and biomechatronics (BioRob), Sao Paulo, 12–15 August 2014, pp.1039–1044. New York: IEEE.

11.

Yoshikawa

Taguchi

Sakamoto

. Trans-radial prosthesis with three opposed fingers. In: Proceedings of the 2013 IEEE/RSJ international conference on intelligent robots and systems (IROS), Tokyo, Japan, 3–7 November 2013, pp.1493–1498. New York: IEEE.

12.

Contreras

Ramirez-Garcia

Gallegos

. Proposal of a mechanism for an electrical elbow prosthesis. In: Proceedings of the 2014 11th international conference on electrical engineering, computing science and automatic control (CCE), Campeche, Mexico, 29 September–3 October 2014, pp.1–5. New York: IEEE.

13.

Kundu

Kiguchi

. Development of a 5 DOF prosthetic arm for above elbow amputees. In: Proceedings of IEEE international conference on mechatronics and automation, Takamatsu, Japan, 5–8 August 2008, pp.207–212. New York: IEEE.

14.

Xiong

Chen

Zhang

. Robot-environment interaction control of a flexible joint light weight robot manipulator. Int J Adv Robot Syst 2012; 9: 76.

15.

Yuan

Sekine

Gonzalez

. Variable impedance control based on impedance estimation model with EMG signals during extension and flexion tasks for a lower limb rehabilitation robotic system. J Nov Physiother 2013; 3: 178.

16.

Laurin-Kovitz

Colgate

Carnes

SDR

. Design of components for programmable passive impedance. In: Proceedings of the 1991 IEEE international conference on robotics and automation, Sacramento, CA, 9–11 April 1991, pp.1476–1481. New York: IEEE.

17.

Morita

Sugano

. Design and development of a new robot joint using a mechanical impedance adjuster. In: Proceedings of IEEE international conference on robotics and automation, Nagoya, Japan, 21–27 May 1995, pp.2469–2475. New York: IEEE.

18.

Morita

Sugano

Mechanical softness and compliance adjustment. J Robot Soc Jpn 1999; 17: 790–794 (in Japanese).

19.

Peng

Song

. Robot-aided upper-limb rehabilitation based on motor imagery EEG. Int J Adv Robot Syst 2011; 8: 88–97.

20.

Mizuno

Tsujiuchi

Koizumi

. Spring-damper model and articulation control of pneumatic artificial muscle actuators. In: Proceedings of the 2011 IEEE international conference on robotics and biomimetics, Karon Beach, Thailand, 7–11 December 2011, pp.1267–1272. New York: IEEE.

21.

Sekine

Xie

Kawamura

. Improvement and quantification of spatial accessibility and disturbance responsiveness of shoulder prosthesis. Int J Adv Robot Syst 2015; 12: 11.

22.

Zhong

Fan

Zhu

. Static modeling for commercial braided pneumatic muscle actuators. Adv Mech Eng 2014; 6: 425217.

23.

Zhong

Fan

Zhu

. One nonlinear PID control to improve the control performance of a manipulator actuated by a pneumatic muscle actuator. Adv Mech Eng 2014; 6: 172782.

24.

Garcia

Arevalo

Sanchez

. Design and development of a biomimetic leg using hybrid actuators. In: Proceedings of the 2011 IEEE/RSJ international conference on intelligent robots and systems (IROS), San Francisco, CA, 25–30 September 2011, pp.1507–1512. New York: IEEE.

25.

Caccese

Ferguson

Lloyd

. Response of an impact test apparatus for fall protective headgear testing using a hybrid-III head/neck assembly. Exp Techniques. Epub ahead of print 4 March 2014. DOI: 10.1111/ext.12079.

26.

Walsh

Rousseau

Hoshizaki

TB.

The influence of impact location and angle on the dynamic impact response of a hybrid III headform. Sports Eng 2011; 13: 135–143.

27.

Sekine

Kita

Designing and testing lightweight shoulder prostheses with hybrid actuators for movements involved in typical activities of daily living and impact absorption. Med Dev Evid Res 2015; 8: 279–294.

28.

Fukaya

Sawada

Oku

. Development of an artificial arm by using a spherical ultrasonic motor. J Jpn Soc Precis Eng 2001; 67: 654–659 (in Japanese).

29.

Miller

Lipschutz

Stubblefield

. Control of a six degree of freedom prosthetic arm after targeted muscle reinnervation surgery. Arch Phys Med Rehab 2008; 89: 2057–2065.

30.

Troncossi

Borghi

Chiossi

. Development of a prosthesis shoulder mechanism for upper limb amputees: application of an original design methodology to optimize functionality and wearability. Med Biol Eng Comput 2009; 47: 523–531.

31.

Troncossi

Gruppioni

Chiossi

. A novel electromechanical shoulder articulation for upper-limb prostheses: from the design to the first clinical application. J Prosthet Orthot 2009; 21: 79–90.

32.

Resnik

Klinger

Etter

The DEKA Arm: its features, functionality, and evolution during the veterans affairs study to optimize the DEKA Arm. Prosthet Orthot Int 2014; 38: 492–504.

33.

Okamoto

Tamura

Koike

. Survey of attitude for amputees of hemi lateral forearm to artificial electric arm. Nat Rehabil Cent Person Disabil Res Bull 2001; 22: 55–61 (in Japanese).

34.

Yokoyama

Takakura

Itoh

. A case report of a high level of upper limb amputee with myoelectric hand. Bull Jpn Soc Prosthet Orthot 2009; 25: 156–159 (in Japanese).

35.

Morales

Badesa

García-Aracil

. Pneumatic robotic systems for upper limb rehabilitation. Med Biol Eng Comput 2011; 49: 1145–1156.

36.

Plettenburg

DH.

Electric versus pneumatic power in hand prostheses for children. J Med Eng Technol 1989; 13: 124–128.

37.

Plettenburg

. Pneumatic actuators: a comparison of energy-to-mass ratio’s. In: Proceedings of the 2005 IEEE 9th international conference on rehabilitation robotics (ICORR 2005), Chicago, IL, 28 June–1 July 2005, pp.545–549. New York: IEEE.

38.

Peerdeman

Smit

Stramigioli

. Evaluation of pneumatic cylinder actuators for hand prostheses. In: Proceedings of the 4th IEEE RAS & EMBS international conference on biomedical robotics and biomechatronics (BioRob), Rome, 24–27 June 2012, pp.1104–1109. New York: IEEE.

39.

Aguilar-Sierra

Salazar

. Design and control of hybrid actuation lower limb exoskeleton. Adv Mech Eng 2015; 7: 1687814015590988.

40.

Sekine

Tsuchiya

Kita

. Designing and testing a hybrid lightweight shoulder prosthesis. In: Proceedings of the 36th annual international conference of the IEEE Engineering in Medicine and Biology Society (EMBC’14), Chicago, IL, 26–30 August 2014, pp.2500–2503. New York: IEEE.

41.

Sekine

Fernandez-Vargas

Hayata

. A hybrid lightweight shoulder prosthesis with an antagonistic mechanism by pneumatic elastic actuators. In: Proceedings of the 2014 international workshop on wearable robotics (WeRob2014), Baiona, Spain, 14–18 September 2014, paper 39.

42.

IMADA Co. Ltd. ZTA-DPU-500N, http://www.forcegauge.net/en/amplifier-en/15331.html (accessed 16 December 2015).

43.

SQUSE. PM-10P, http://www.squse.co.jp/product/detail.php?id=9 (in Japanese, accessed 16 December 2015).

44.

Futaba Corporation. RS405CB, http://www.futaba.co.jp/en/robot/5350/RS40x.html (accessed 16 December 2015).

45.

Ohnishi

Improving the usability of myoelectric controls and upper limb prostheses. Bull Jpn Soc Prosthet Orthot 2011; 27: 84–88 (in Japanese).

46.

Chin

Myoelectric prostheses: current status and problems to be solved, a rehabilitation strategy for higher level amputation patients, and the future outlook. Jpn J Rehabil Med 2012; 49: 31–36 (in Japanese).

47.

Ohnishi

Tajima

Saito

A shape memory alloy actuator system for a passive shoulder disarticulation prosthesis. J Life Support Eng 2002; 14: 20−25 (in Japanese).

48.

Wen

Murphy

Stability analysis of position and force control for robot arms. IEEE T Automat Contr 1991; 36: 365–370.

49.

Sekine

Sugimori

Xie

. Dynamical analysis of trunk load caused by different weight distribution of prosthetic arm systems. In: Proceedings of the 15th IASTED international conference on control and applications (CA 2013), Honolulu, HI, 26–28 August 2013, pp.15–21. Calgary, AB, Canada: ACTA Press.