Côme Butin
email: come.butin@orthopus.com

Damien Chablat
email: damien.chablat@cnrs.fr

Yannick Aoustin
email: yannick.aoustin@univ-nantes.fr

David Gouaillier
email: david.gouaillier@orthopus.com

Design of a Two

Keywords: Hand prosthesis, motion transmission, wrap spring

Introduction

Myoelectric hand prostheses are developed since the 1970s to our days in various forms. The first myoelectric prostheses were designed with one Degree of Actuation (DoA) and were suitable to realize only the tridigital pinch. Tridigital hands such as the VariPlus Speed from Ottobock manufacture 2 or the Myo Kinisi hand from Steeper manufacture 3 are still sold, and are usually appreciated for their force, their speed and their robustness. The most advanced commercially available prostheses have more complex kinematics with up to six actuators and sub-actuation mechanisms to drive 10 or 11 joints, like the i-Limb Touch Bionics from Össur manufacture 4 , the hand prosthesis from TASKA manufacture 5 , and the hand prosthesis from COVVI manufacture 6 . These prostheses are more anthropomorphic, but are developing less force and speed [START_REF] Belter | Mechanical design and performance specifications of anthropomorphic prosthetic hands: A review[END_REF] than the tridigital prostheses, and the system complexity leads to a lack of mechanical robustness. Their price is prohibiting for countries without a powerful health care system.

In the aim of designing an accessible prosthetic hand (affordable, easy-to-use, robust, easy-to-repair), limiting the number of actuators seems to be a legitimate choice by decreasing the complexity of the hand, thus reducing its price and the weight of the battery, increasing the robustness, and reducing the control strategy complexity for the user. Few commercial hands exist as hybrid between polydigital and tridigital hands with one or two actuators, such as the Michelangelo from Ottobock manufacture, the MyHand from Hy5 manufacture 7 and the Adam's Hand from BionIT Labs manufacture 8 . These prostheses remain complex, and cannot be afforded in low and middle income countries (LMIC).

A lot of academic works proposed single actuator prostheses [START_REF] Belter | Novel differential mechanism enabling two DOF from a single actuator: Application to a prosthetic hand[END_REF][START_REF] Leddy | Preliminary Design and Evaluation of a Single-Actuator Anthropomorphic Prosthetic Hand with Multiple Distinct Grasp Types[END_REF][START_REF] Wattanasiri | Design of Multi-Grip Patterns Prosthetic Hand with Single Actuator[END_REF][START_REF] Zheng | Design of a Low-Cost and Humanoid Myoelectric Prosthetic Hand Driven by a Single Actuator to Realize Basic Hand Functions[END_REF][START_REF] Xu | A single-actuator prosthetic hand using a continuum differential mechanism[END_REF][START_REF] Laffranchi | The Hannes hand prosthesis replicates the key biological properties of the human hand[END_REF]. These works are focusing on sub-actuation mechanisms and differential mechanisms to adapt the force exerted by each finger on the grasped object. Their pinching forces are poor (from 3.5N [START_REF] Leddy | Preliminary Design and Evaluation of a Single-Actuator Anthropomorphic Prosthetic Hand with Multiple Distinct Grasp Types[END_REF] to 34.5N [START_REF] Wattanasiri | Design of Multi-Grip Patterns Prosthetic Hand with Single Actuator[END_REF] -only power grasp is documented in [START_REF] Laffranchi | The Hannes hand prosthesis replicates the key biological properties of the human hand[END_REF]) compared to the 78N measured on the Michelangelo [START_REF] Belter | Mechanical design and performance specifications of anthropomorphic prosthetic hands: A review[END_REF] and the minimum 68N prescribed for Activities of Daily Living (ADL) [START_REF] Weir | Design of Artificial Arms and Hands for Prosthetic Applications[END_REF]. Their speed is also poor (0.47s [START_REF] Leddy | Preliminary Design and Evaluation of a Single-Actuator Anthropomorphic Prosthetic Hand with Multiple Distinct Grasp Types[END_REF] to 1.4s [START_REF] Wattanasiri | Design of Multi-Grip Patterns Prosthetic Hand with Single Actuator[END_REF] of closing time) compared to the performances of the commercially available hands (300mm/s, ~0.3s closing time for the Michelangelo and the VariPlus Speed). It can be noted that the fastest hand of the previous references is the weakest in terms of applicable efforts, while the one that applies the strongest efforts is the slowest.

Using more powerful motors to achieve better performance is not a reliable option. Increasing the motor power means increasing the cost of the prosthesis, its weight, its dimensions, and the size and weight of the battery system. Instead, the optimization of the energy consumption is preferred.

Considering that most of the energy is lost by Joule effect in the motor and mechanical friction, higher performances can be obtained with a same amount of energy by optimizing the transmission of the system and the operating point of the motor. Indeed, a myoelectric hand is working at two different operating points. For each grasp sequence, the open hand is firstly closing its fingers at a given speed with no external load until the object contacts the fingers. Then, the fingers apply an important force to securely hold the object, at very low speed. This characteristic is useful to optimize the energy consumption.

As pointed out in [START_REF] Weir | Design of Artificial Arms and Hands for Prosthetic Applications[END_REF] many years ago, Ottobock strategy is to use an "automatic transmission", changing gear ratio when a high torque is detected by a spring. To the best author's knowledge, Ottobock equivalent solutions have never been analyzed in the academic literature, but patents have been submitted [START_REF] Puchhammer | Clutch module for prostheses[END_REF]. The developed system transforms a multi-turn rotary movement into a second multi-turn rotary movement. This mechanism needs an important number of complex and miniature mechanical parts, requiring precision machining.

Another solution can be inspired by the different types of Continuous Variable Transmission (CVT) where the reduction ratio is varying continuously with the transmitted torque. Most of the CVT have been developed for automotive industry, and their working principle is not suitable for affordable prosthesis where the num-ber and size of parts must be minimized to meet weight, size and price requirements. Only few different CVT have been proposed for prosthetic hands and robotics [START_REF] Kernbaum | An ultra-compact infinitely variable transmission for robotics[END_REF].

Takaki proposed a Rotary-to-Rotary CVT based on a five-bar linkage and a preconstrained spring [START_REF] Takaki | Development of a 2-d.o.f. finger using load-sensitive continuously variable transmissions and ultrasonic motors[END_REF]. While this system allows for a threefold increase in maximum finger force for a same input power and with pretty simple manufactured parts, this linkage does not provide a constant behavior on the finger range. A singularity appears for a particular position of the fingers, and the mechanism impacts directly all the hand kinematics. More recently, Liu adapted this linkage using a slider crank mechanism [START_REF] Liu | Design of a Lightweight Single-Actuator Multi-Grasp Prosthetic Hand with Force Magnification[END_REF], with a force gain between two and four along the finger range. While the singularity has been removed, force magnification does not stay constant and is suitable only for prosthetic hands using translation movement.

Belter proposed a Rotary-to-Linear CVT [START_REF] Belter | A Passively Adaptive Rotary-to-Linear Continuously Variable Transmission[END_REF] using a mechanism adapted from a lead screw where the pitch can vary depending on the force applied on the screw. In this mechanism, the screw and the nut are composed of smooth components to enable pitch variation, and the sliding is avoided by applying an initial force between the contacting bodies. The solution is suitable only for prosthetic hands using translation movement, and the maximum mechanical efficiency is comprised between 18% and 30% that limits the benefit of this transmission.

Finally, different works have been developed for tendon-based transmission. Matsuhita et al. [START_REF] Matsushita | Development of Drum CVT for a wire-driven robot hand[END_REF] and O'brien et al. [START_REF] O'brien | Elastomeric passive transmission for autonomous force-velocity adaptation applied to 3D-printed prosthetics[END_REF] are using drums with a varying diameter to adapt the tension and the speed of the wounded wire to the load. Shin et al. [START_REF] Shin | A Robot Finger Design Using a Dual-Mode Twisting Mechanism to Achieve High-Speed Motion and Large Grasping Force[END_REF] use an actuator that twist a two-wire tendon to transform a rotary motion into a linear motion. The transmission ratio can be adjusted by twisting the two wires between each other (small reduction) or around a shaft (high reduction). A mechanism is proposed to switch between two modes depending on load. Theses works are specific to tendonbased prostheses which is not preferred in commercial prostheses [START_REF] Belter | Mechanical design and performance specifications of anthropomorphic prosthetic hands: A review[END_REF] for the difficulties of transmitting high forces with robustness.

Others solutions are using two actuators [START_REF] Weir | Design of Artificial Arms and Hands for Prosthetic Applications[END_REF][START_REF] Naclerio | Low-Cost, Continuously Variable, Strain Wave Transmission Using Gecko-Inspired Adhesives[END_REF] but are not presented here while adding a second actuator will increase cost, weight, complexity, and probably energy consumption.

To solve the energy consumption issue caused by the use of a single actuator and by the need for high performances, we propose here a novel Load Adaptive Variable Transmission (LAVT). This LAVT exhibits similar performances to Ottobock's solutions with a multi-turn Rotary-to-Rotary transmission and two different speeds, capable of varying its reduction ratio under a given load. Thus, this mechanism could be associated with all kind of transmissions that use rotary actuator as input. Since this mechanism has been designed in the aim to be as simple as possible, it is composed of only few simple mechanical parts. It is composed of a planetary gear train (PGT) working in two different modes, and a selector clutch using wrap spring clutch, which switches the working mode of the PGT at a given torque. The design steps have been detailed to enable the adaptation of the mechanism to other applications. A first prototype has been developed as a proof of concept. This work was conducted in collaboration with the BionicoHand project [START_REF]Projets: Bionicohand WIKILAB[END_REF], which aims to develop an accessible Open Source prosthesis with rigid fingers (no DIP and PIP joint) with one single actuator. However, the solution proposed in this paper is suitable for any prosthetic hand or robotic gripper with one DoA requiring high power for low energy consumption. This paper is outlined as follows. The different parameters of motorization that minimize energy consumption are analyzed in Section 2, and we show the advantages of the LAVT. Then, an architecture of LAVT, and a method of size it according to specifications are proposed Section 3. Section 4, an experimental protocol on a developed prototype is proposed, and the results are detailed and discussed. Finally, Section 5 offers conclusions and direction for future work. In a user-centric approach, it is important to start from the user needs. The prosthesis performances are a selection criterion for the user, but can also be a reason for prosthesis abandonment. In this work, we are interested in :

• the maximal opening width of the hand;

• the closing time, or the speed of the fingers;

• the grasping force and stability, which ensure to hold objects strongly.

It is important to keep in mind that the grasping stability is related to the grasping force, but also to other parameters such the material of the objects, the finger joints, the number of contact points or the distribution of the force between these points.

Grasping

Force and Speed Definition. Grasping force and speed are key metrics to qualify the performances of robotic hands. While a metric to measure grasping stability is more complex to obtain, grasping force is also a key specification for the designer. These performances are often given by prosthesis manufacturers, but they are not clearly defined and seem to be different between companies and products.

A simple approach to define these metrics is to consider a pinch with two opposite groups of fingers (like a myoelectric gripper or a tridigital hand), with only two contact points located at finger tips. Thus, the analysis stays planar. Let us call 𝑝 𝑈 and 𝑝 𝑇 the contact points at tip of the upper fingers and the thumb respectively, and 𝜃 the position of the fingers, as shown on Fig. 1 for a tridigital prosthetic hand.

The linear speed 𝑉 is defined as the approach speed between the two contact points 𝑝 𝑈 and 𝑝 𝑇 :

𝑉 (𝜃) = d∥ -----→ 𝑝 𝑈 𝑝 𝑇 ∥ d𝑡 (1)
Then, the pinching force is defined as the force exerted by the upper fingers on the thumb, equal and opposite to force exerted by the thumb on the upper fingers. Considering the unit vector

- → 𝑢 = -----→ 𝑝 𝑈 𝑝 𝑇 ∥ 𝑝 𝑈 𝑝 𝑇 ∥ , 𝐹 (𝜃) = 𝐹 𝑈 /𝑇 - → 𝑢 (2)
This choice is motivated by the aims of motorization sizing and optimization, since the grasping power 𝑃 𝐺 (𝜃) is equal to the product of the speed 𝑉 (𝜃) and the force 𝐹 (𝜃). This choice also allows to get rid of the kinematics and transmission between fingers in a first sizing iteration, since for a given constant torque and a constant rotation speed of the motorization, the grasping power 𝑃 𝐺 will no longer depend on 𝜃, according to the principle of virtual power.

We can remark that these metrics are not suitable for hands with articulated fingers that enable more than two contact points on objects. In that case, a metric is proposed in [START_REF] Falco | Performance Metrics and Test Methods for Robotic Hands[END_REF], where our definition remains compatible in the case of two contact points.

Performance

Index. An index is proposed in this section to characterize the needs for motorization sizing. The maximal grasping force 𝐹 𝑚𝑎𝑥 occurs when the object is grasped at very low speed, and the maximal speed 𝑉 𝑚𝑎𝑥 occurs in the approaching phase at very low load. On these two phases, the grasping power 𝑃 𝐺 previously introduced stands near to zero, it is not appropriate to size a motor and its reduction. We propose instead a Performance Index 𝑃 𝐼 , expressed in N.mm/s and defined as :

𝑃 𝐼 = 𝑉 𝑚𝑎𝑥 (𝜃) • 𝐹 𝑚𝑎𝑥 (𝜃) ∀𝜃 (3)
The performance index is valid for all angular values 𝜃, but a single angular value 𝜃 has to be chosen to evaluate 𝑉 𝑚𝑎𝑥 and 𝐹 𝑚𝑎𝑥 at the same point, for example at mid-range, or for an object with a specific width.

According to the principle of virtual power, this performance index also characterizes the motor and its transmission in terms of maximal torque 𝜏 𝑚𝑎𝑥 and maximal rotation speed 𝜔 𝑚𝑎𝑥 , with 𝑙 𝑒𝑞 (𝜃) the kinematic equivalent lever such that 𝑉 (𝜃) = 𝜔 • 𝑙 𝑒𝑞 (𝜃), and thus 𝐹 (𝜃) • 𝑙 𝑒𝑞 (𝜃) = 𝜏.

𝑃 𝐼 = 𝑉 𝑚𝑎𝑥 (𝜃) 𝑙 𝑒𝑞 (𝜃) • 𝐹 𝑚𝑎𝑥 (𝜃) • 𝑙 𝑒𝑞 (𝜃) = 𝜔 𝑚𝑎𝑥 • 𝜏 𝑚𝑎𝑥 (4)
In this way, the motor and its transmission can be sized independently of the kinematics.

Dissipated Energy at Grasp.

A way to evaluate the minimal needed energy or power needed to grasp an object is to evaluate the power dissipated in an object due to its elasticity during grasping.

A grasping task does not require a high mechanical power, since speed is not necessary at the same time as force. It can be remarked that most of the grasped objects of daily life are highly rigid and are not storing or dissipating a lot of energy compared to the energy available in the battery. Considering an object as an elastic body, the work 𝑊 to deform it can be from its stiffness coefficient 𝐾, its displacement variable Δ𝑥 and 𝐹 the force applied on it.

𝑊 = 1 2 𝐾Δ𝑥 2 = 𝐹 2 2𝐾 (5)
As an order of magnitude of the equation parameters, we selected a reusable polymer water cup to represent a low stiffness daily life object, and measured the work needed to grasp it with a force of 80N. By applying this force ten times on the border of the object, we measured an average displacement of 30mm, leading to a rough approximation of the stiffness coefficient 𝐾=2.5N/mm. This cup stores an energy 𝑊=1.3J, while a typical Li-ion Battery 7.2V 1000mAh is storing 26kJ, meaning 20'000 grasping tasks.

Most of the objects are stiffer, and a force of 80N on a water cup to hold it firmly is voluntarily overestimated.

By squeezing this object in 0.3 seconds, a mean power of 4.3W will be necessary, while taking the maximal specifications of the Michelangelo (80N, 300mm/s) will lead to a power of 24W.

Power Analysis in Motor and Transmission.

In the previous analyses, we showed that only few energy is needed for grasping, and that the Performance Index can ensure to attain the desired performances down to the reduction ratio, independently of the kinematics. We analyze in this section the effect of each parameter of the motorization in order to optimize the energy consumption while attaining desired performances.

The chosen model of motorization is composed of a brushed DC motor for its affordability and its simplicity of control, and a transmission composed of several stages of geared reducers.

The DC motor is characterized by its back-EMF constant 𝑘 𝐸 , approximately equal to its torque constant 𝑘 𝑀 ≈ 𝑘 𝐸 = 𝐾, and its resistance 𝑅. The values of maximal torque and associated maximal current mainly come from the thermal limits of the motor, although the motor maximal thermal current can be exceeded over a short time with an adapted control strategy. The maximal admissible speed provides the maximal supply voltage. The transmission is characterized by its global reduction ratio 𝑅 𝑔 = 𝜔 𝑜𝑢𝑡 /𝜔 𝑚𝑜𝑡 and its global efficiency coefficient 𝜂 𝑔 .

Assuming that the energy loss is negligible during the approach and that back EMF is negligible at grasping, we can compare the electrical power 𝑃 𝐸 consumed by the motor at stall condition with the Performance Index of the system.

𝑃 𝐸 = 𝑅𝐼 2 𝑚𝑎𝑥 = 𝑅 𝜏 2 𝑚𝑜𝑡 ,𝑚𝑎𝑥 𝑘 2 𝑀 = 𝑅 𝐾 2 𝑅 2 𝑔 𝜂 2 𝑔 𝜏 2 𝑚𝑎𝑥 (6)
An Energy Loss Index 𝐸 𝐿𝐼 can be introduced:

𝐸 𝐿𝐼 = 𝑃 𝐸 𝑃 𝐼 = 𝑅 𝐾 2 𝑅 2 𝑔 𝜂 2 𝑔 𝜏 𝑚𝑎𝑥 𝜔 𝑚𝑎𝑥 (7)
To minimize 𝐸 𝐿𝐼 according to Eq. ( 7), different terms can be minimized. The first term 𝑅/𝐾 2 corresponds to the motor parameters. It has been observed that this term stays approximately constant (around 10 to 20% of variation) for different models, different nominal voltages and different coefficients 𝐾, on a given technology of brushed DC motor and for a given range of power. Taking care of minimizing this value during motor choice can be a good reflex, but it will not be a major factor.

The second term 𝑅 2 𝑔 /𝜂 2 𝑔 corresponds to transmission parameters. A first intuitive lever is the maximization of the mechanical efficiency 𝜂 𝑔 . It can be remarked that the effect is squared, so low efficiency transmissions like worm gear reducers have to be avoided. The reduction ratio 𝑅 𝑔 also plays an important role. An important reduction is needed to minimize 𝐸 𝐿𝐼 , that is to say a motor with a low torque and a high speed. However, the speed is limited by the mechanical components used, and the motor used near its speed limit (around 9000 to 10000 RPM for classical DC brushed motors). It has to be kept in mind that a high speed lowers the lifetime of the motor, which can be a design issue.

Finally, the third term 𝜏 𝑚𝑎𝑥 𝜔 𝑚𝑎𝑥 is fixed by the specifications and cannot be changed.

Introduction of Variable Transmission.

The previous analysis shows that an optimization of some parameters is possible to reduce energy consumption at given performances. However, the minimization is limited at some point by the cost of improving efficiency and by the maximal speed of affordable motors.

Other solutions have been implemented, by varying the reduction ratio 𝑅 𝑔 between the approach phase (𝑅 𝑔 = 𝑅 𝐼 ) and the grasping phase (𝑅 𝑔 = 𝑅 𝐼 𝐼 ). In these conditions, Eq. ( 7) is changed as

/ 3
𝐸 𝐿𝐼 = 𝑃 𝐸 𝑃 𝐼 = 𝑅 𝐾 2 𝑅 2 𝐼 𝐼 𝜂 2 𝑔 𝜏 𝑚𝑎𝑥 𝜔 𝑚𝑎𝑥 (8)
In this case, the minimization of 𝑅 𝐼 𝐼 is no longer limited directly by the motor speed. With the ratio variation 𝑄 = 𝑅 𝐼 /𝑅 𝐼 𝐼 , 𝑅 𝐼 can be lowered by a factor of 𝑄 to maintain the same output speed without exceeding the motor maximal speed. The minimization of 𝐸 𝐿𝐼 is then by a factor of 𝑄 2 . For example, a ratio variation of five between the two phases can lower the energy consumption by 25 while keeping same performances for the user. This result highly motivates the development of a variable transmission presented in the next sections.

Load Adaptative Variable Gear Train Analysis

3.1 Mechanism Principle and Architecture. The Load Adaptive Variable Transmission presented in this paper is a twospeed reducer where a transition between two speeds occurs when the transmitted torque is exceeding a predefined torque. The LAVT is based on a planetary gear train where parts can be blocked together or let free through a clutch, activated by the transmitted torque. Figure 2 shows the kinematic diagram in the two different modes. The planetary gear train is composed of the chassis 0 , the sun gear 1 , the carrier 2 , the ring gear 3 and the satellites 4 . The sun gear acts as the mechanism input. The carrier acts as the output.

In mode I, for low transmitted torque, the ring gear 3 is blocked on the carrier 2 . It produces that the sun gear, the satellites, the carrier and the ring gear are fixed together. There is no reduction in mode I.

In mode II, for high transmitted torque, the ring gear 3 is blocked on the chassis 0 . The speed ratio 𝑅 of the planetary train in mode II is given by the following equation:

𝑅 = 𝜔 𝑜𝑢𝑡 𝜔 𝑖𝑛 = 𝜏 𝑖𝑛 𝜏 𝑜𝑢𝑡 = 𝑍 1 𝑍 3 + 𝑍 1 (9)
where 𝜏 𝑖𝑛 and 𝜏 𝑜𝑢𝑡 are the input and output torques, respectively and 𝜔 𝑖𝑛𝑡 and 𝜔 𝑜𝑢𝑡 are the input and output angular velocities, The torque ratio of the PGT is 1/𝑅 when considering negligible the friction losses on the teeth.

Selector Clutch using Wrap Spring

Clutch. This LAVT relies on a selector clutch that locks the ring gear either on ring gear or carrier depending on the transmitted torque. The developed clutch is based on wrap spring clutches.

Wrap spring clutches can be used in many applications, such as overrunning clutches (or one-way clutch), indexing clutches, or clutch brakes. It consists of a coil spring between two rotating bodies (input and output), where the bodies are in contact of the spring either on internal or external surfaces, as shown on Fig. 3 [START_REF] Lowery | How to do more with wrapped-spring clutches[END_REF][START_REF] Roach | Evaluation and comparison of alternative compliant overrunning clutch designs[END_REF]. Their working principle is standing on the Capstan effect [START_REF] Cronin | Variability in output torque of capstan and wrap spring elements[END_REF] that permits to amplify a friction pressure along a coil by applying a small tension at one end. The resulting torque is increasing exponentially to the number of active coils 𝑁 and the friction coefficient 𝜇.

The simplest application of wrap spring clutches are overrunning clutches (Fig. 3) where the input can transmit high torque to the output in one way, and is slipping in the other way. In the free way, a small amount of friction has to be countered, while in the blocking way this friction is largely amplified. The initial frictional torque 𝜏 0 can be produced by a counter torque at the free end. The slipping torque limit in the blocking way 𝜏 𝑏 , which also depends on the spring wire radius 𝑟 𝑠 and the spring neutral radius 𝑟 𝑛 , is given by Cronin [START_REF] Cronin | Variability in output torque of capstan and wrap spring elements[END_REF] in the following equation:

𝜏 𝑏 = 𝜏 0 e 2 𝜋 𝑁 𝜇 𝜌 1+𝜌 ≈ 𝜏 0 e 2 𝜋 𝑁 𝜇 with 𝜌 = 𝑟 𝑛 𝑟 𝑠 ≫ 1 (10)
The initial frictional torque can be either produced by a small interference 𝛿𝑟 between the spring internal radius 𝑟 0 = 𝑟 𝑛 -𝑟 𝑠 and the body radius 𝑟. The torque slipping limits have been expressed by Wiebusch [START_REF] Wiebusch | The Spring Clutch[END_REF] and Wahl [START_REF] Wahl | Discussion: "The Spring Clutch[END_REF] in blocking way 𝜏 𝑏 and in the free way 𝜏 𝑓 , considering an internal clutch with a high radius ratio 𝜌 as follows.

𝜏 𝑏 = 𝐸 𝐼 𝑟 2 𝑛 𝛿𝑟 (e 2 𝜋 𝑁 𝜇 -1) (11)
𝜏 𝑓 = 𝐸 𝐼 𝑟 2 𝑛 𝛿𝑟 (1 -e -2 𝜋 𝑁 𝜇 ) ≈ 𝐸 𝐼 𝑟 2 𝑛 𝛿𝑟, with 𝑁 𝜇 > 1 (12)
where 𝐸 and 𝐼 represent, respectively, Young's modulus and the moment cross-section of the spring. It has been noticed that in the blocking way, measurements can lead to errors with respect to the results given by Eq. ( 11) up to 20% [START_REF] Wiebusch | The Spring Clutch[END_REF]. Several problems can explain differences such as chosen hypotheses [START_REF] Wahl | Discussion: "The Spring Clutch[END_REF] or friction coefficient variability [START_REF] Cronin | Variability in output torque of capstan and wrap spring elements[END_REF]. In the free way, the theory is more reliable.

The curved beam theory [START_REF] Wahl | Discussion: "The Spring Clutch[END_REF] also gives us the radial displacement 𝑟 𝑖 for a free spring under a given torque 𝜏 𝑖 in:

𝜏 𝑖 = 𝐸 𝐼 𝑟 2 𝑛 𝛿𝑟 𝑖 . ( 13
)
The form of this equation is similar to that of Eq. [START_REF] Liu | Design of a Lightweight Single-Actuator Multi-Grasp Prosthetic Hand with Force Magnification[END_REF]. By using the same principle, it is possible to create a selector clutch by combining an internal clutch and an external wrap spring clutch on the same spring to switch between Mode I and Mode II. Figure 4 shows the profile of the spring. Under no load, the spring is preloaded on the body A. This preload creates a friction as shown in Eq. ( 12), which permits transferring low torque from surface S to A. When load is applied to the spring through body S, the spring is expanding in diameter until contacting the surface B. At this point, the friction on the surface B, greater than the slipping limit on the surface A, makes the spring block on the surface B while A begins to slip. This type of clutch selector is used in Ottobock's Greifer, combined with a more complex transmission than the simple PGT proposed here.

This selector clutch is working only in one way, where the spring is expanding under torque. In the other way, the spring will be blocked on the friction surface A that makes LAVT blocked in mode I. Thus, this working is acceptable for a grasping task, where high torque is only useful at the end of the fingers closing while opening can be realized at low torque only.

Wrap spring clutch seems to be an interesting technical solution for accessible prosthetic hand, with a good durability, a high torque to dimensions ratio and a low manufacturing cost [START_REF] King | Alternator Pulley with Integral Overrunning Clutch for Reduction of Belt Noise[END_REF]. The torque applied by the satellites 4 on the ring gear 3 , noted 𝜏 4/3 and the torque applied by the satellites 4 on the carrier 2 , noted 𝜏 4/2 can be expressed from the torque applied by the satellites 4 on the sun shaft 1 , noted 𝜏 4/1 at static equilibrium.

Loads and Efficiency Analysis.

𝜏 4/3 = - ( 1 𝑅 -1 ) 𝜏 1/4 ( 14
)
𝜏 4/2 = 1 𝑅 𝜏 1/4 (15)
In mode I, when the spring is only in contact with the carrier, the output torque 𝜏 𝑜𝑢𝑡 can be expressed from the input torque 𝜏 𝑖𝑛 as follows:

𝜏 𝑜𝑢𝑡 = 𝜏 3/2 + 𝜏 4/2 = 𝜏 4/3 + 𝜏 4/2 = -𝜏 𝑖𝑛 ( 1 𝑅 -1 ) + 𝜏 𝑖𝑛 1 𝑅 = 𝜏 𝑖𝑛 (16)
In mode II, when the spring is contacting the chassis and is slipping on the carrier, the output torque can be expressed from the input torque as follows:

𝜏 𝑜𝑢𝑡 = 𝜏 𝑏 3/2 + 𝜏 4/2 = -𝜏 𝑏 2/3 + 𝜏 𝑖𝑛 1 𝑅 (17)
While input torque is entirely transmitted to the output in mode I, providing an efficiency coefficient 𝜂 = 1 by assuming an ideal PGT, a constant friction torque remains in mode II. In this mode, the efficiency coefficient is expressed as follows: From Eq. ( 13), the torque on the spring needed to contact the surface B is known. This transition torque 𝜏 𝑡 applied on the spring can be expressed as a transition torque from the input shaft:

𝜂 = 𝑃 𝑜𝑢𝑡 𝑃 𝑖𝑛 = 𝜔 𝑜𝑢𝑡 𝜔 𝑖𝑛 𝜏 𝑜𝑢𝑡 𝜏 𝑖𝑛
𝜏 2/3 = 𝜏 𝑡 ⇔ 𝜏 𝑖𝑛 = 𝜏 𝑡 𝑖𝑛 = ( 𝑅 1 -𝑅 ) 𝜏 𝑡 (19)
Figure 6 presents the output torque 𝜏 𝑜𝑢𝑡 for a normalized input torque 𝜏 𝑖𝑛 between zero and one, according to Eq. ( 16) and Eq. [START_REF] Naclerio | Low-Cost, Continuously Variable, Strain Wave Transmission Using Gecko-Inspired Adhesives[END_REF]. Five different pairs of speed ratio 𝑅 and 𝜏 𝑡 are chosen to show the impacts of these two parameters. The sliding torque 𝜏 𝑏 = 𝜏 𝑏 2/3 is set such that 𝜏 𝑏 = 𝜏 𝑡 that is a result of the sizing process and corresponds to its optimal value as it will be explained in Section 3.4. Figure 6 shows that a higher output torque 𝜏 𝑚𝑎𝑥 𝑜𝑢𝑡 can be provided by decreasing 𝑅, or by decreasing the transition torque 𝜏 𝑡 .

The efficiency is presented on Fig. 7 where 𝜂 = 1 during the Mode I phase and 𝜂 is calculated from Eq. ( 18) during the Mode II. The different configurations are plotted for a same range of the input torque 𝜏 𝑖𝑛 , explaining the different ranges of 𝜏 𝑜𝑢𝑡 . Figure 7 shows that the principal effect of decreasing 𝑅 is an enlargement of the graph in mode II, corresponding to the higher increase rate / 5 Fig. 6 τ out as function of τ i n at quasi-static state for five different pairs of (R, τ t ), with τ b = τ t on Fig. 6. A slight decrease of the efficiency at output maximal torque can be noticed but stays small. Conversely, 𝜏 𝑜𝑢𝑡 𝑚𝑎𝑥 is highly degraded by an increase of the transition torque 𝜏 𝑡 .

A first approach to optimize the energetic efficiency of this mechanism would be to minimize the reduction ratio and the transition torque.

Sizing Process. The sizing process is organized in five main steps.

Reduction ratio and transition of the torque. To size the system, the reduction ratio 𝑅 and the transition torque 𝜏 𝑡 have to be chosen. These two parameters are affecting the maximal torque available and the speed in mode II, but also the efficiency of the system, and the minimal torque available in mode I before transition (Eqs. ( 16)-( 19)).

As seen in Section 3.3, it is advised to lower 𝑅 and 𝜏 𝑡 to obtain a high maximal output torque with a high efficiency. Thus, these two parameters have a lower limit.

A very low 𝑅 is difficult to realize with a standard PGT (around 1/8). Furthermore, a too low value of 𝑅 can lower the speed in mode II too much, producing a sensation of control loss by the user.

The transition torque at output 𝜏 𝑡 𝑜𝑢𝑡 should stay high enough to overcome friction and glove elasticity without speed loss.

Planetary gear train sizing. From the chosen reduction ratio, the planetary gear train can be sized. The number of teeth of the sun gear 𝑍 1 , of the satellites 𝑍 4 and of the ring gear 𝑍 3 = 2𝑍 4 + 𝑍 1 are constrained:

• manufacturing process of gears and cost constrain the gears to have at least eight to ten teeth, and a module as high as possible;

• the radius of the ring gear should stay as low as possible to keep the volume of the mechanism low;

• the number of satellites 𝑁 𝑠𝑎𝑡 is preferably three, or four. Using two satellites is less favorable for force distribution on sun gear, requiring bigger teeth and producing more vibrations. Using more than four satellites is not advised for limiting friction and keeping an efficient gearbox;

• assembly is possible only if (𝑍 1 + 𝑍 4 ) mod 𝑁 𝑠𝑎𝑡 = 0;

• the radius, module and width of the gears should be adapted to the transmitted torque. Under these constrains, all numerical values of the reduction ratio 𝑅 given by Eq. ( 9) are not realizable, especially for 𝑅 < 1/5.

Spring wire sizing. The wire diameter should be selected to handle the stress induced in the spring during deformation. When the spring is not contacting the outer ring, it can be represented as a curved beam subjected to a torque. The following equation gives the stress 𝜎 𝑚𝑎𝑥 of a spring with an inertia 𝐼 under a torque 𝜏 𝑚𝑎𝑥 .

𝜎 𝑚𝑎𝑥 = 𝑟 𝑠 𝐼 𝑘 𝑏 𝜏 𝑚𝑎𝑥 < 𝑅 𝑒 𝑠 ( 20
)
where 𝑠 is a safety coefficient and 𝑅 𝑒 the elastic limit.

For circular section, it gives:

𝜎 𝑚𝑎𝑥 = 4𝑘 𝑏 𝜋𝑟 3 𝑠 𝜏 𝑚𝑎𝑥 . (21)
Here 𝑘 𝑏 is the correction factor of the curved beam theory defined as:

𝑘 𝑏 = 4𝜌 2 -𝜌 -1 4𝜌(𝜌 -1) with 𝜌 = 𝑟 𝑛 𝑟 𝑠 (22)
While Eq. ( 22) involves 𝑟 𝑛 which has not been determined yet, an approximation of 𝑘 𝑏 can be used in a first iteration. For 𝜌 > 8, taking 𝑘 𝑏 = 1.1 permits to respect Eq. [START_REF] Lowery | How to do more with wrapped-spring clutches[END_REF].

The wire diameter should be kept as low as possible to maximize a displacement under a given torque, and thus reducing the needed manufacturing precision. A further analysis is needed to validate the stress in the spring under constraints on the outer ring.

Spring diameter and friction surfaces sizing. Once the wire diameter is selected, the spring diameter and the diameter of the two friction surfaces can be chosen.

The transition torque 𝜏 𝑡 can be expressed from Eq. ( 13) and the radius 𝑟 𝑏 of the contact surface B.

𝜏 𝑡 = 𝐸 𝐼 𝑟 2 𝑛 𝛿𝑟 𝑏 (23)
The input and output torques at transition 𝜏 𝑡 𝑖𝑛 and 𝜏 𝑡 𝑜𝑢𝑡 can be expressed:

𝜏 𝑡 𝑖𝑛 = 𝜏 𝑡 𝑜𝑢𝑡 = 𝑅𝐸 𝐼 (1 -𝑅)𝑟 2 𝑛 𝛿𝑟 𝑏 (24)
Thus, for a given torque, different parameter pairs (𝑟 𝑛 , 𝛿𝑟 𝑏 ) can be chosen. Choosing a high 𝛿𝑟 𝑏 can improve the robustness of the system with respect to manufacturing inaccuracies, but increases the volume of the system. To ensure contact, the spring has to contact body B before sliding on body A. At sliding condition, the intermediate portion of spring will attain an internal radius equal to 𝑟 𝑏 . Radius 𝑟 𝑎 has to be set as close as possible of 𝑟 𝑏 to reduce the friction torque 𝜏 𝑏 down to 𝜏 𝑡 , but it has to stay greater with a small clearance to ensure a correct transition. This torque is calculated with Eq. ( 12) and is slightly higher than the transition torque 𝜏 𝑡 .

𝜏 𝑏 = 𝐸 𝐼 𝑟 2 𝑛 𝛿𝑟 𝑎 (25)
Spring length and material choice. When the spring is contacting the body B, sliding torque between S and A has to be lower than sliding torque between S and B, as follows:

𝐸 𝐼 𝑟 2 𝑛 𝛿𝑟 𝑎 < 𝐸 𝐼 𝑟 2 𝑛 𝛿𝑟 𝑏 (e 2 𝜋 𝑁 𝐵 𝜇 -1) (26)
with 𝑁 𝐴 and 𝑁 𝐵 representing the number of spires contacting surfaces A and B respectively. The interference radius 𝛿𝑟 𝑎 and 𝛿𝑟 𝑏 are set close to each other, so a simplification can be made.

e 2 𝜋 𝑁 𝐵 𝜇 > 2 ⇔ 𝑁 𝐵 𝜇 > ln(2) 2𝜋 ≈ 0.11 (27)
In mode II, the torque between the spring and the surface B should stay under the sliding limit expressed in Eq. ( 10) with 𝜏 0 = 𝜏 𝑏 the friction torque between the spring and the surface A.

𝜏 𝑏 (e 2 𝜋 𝑁 𝐵 𝜇 -1) > 𝜏 𝑚𝑎𝑥 𝑖𝑛 1 -𝑅 𝑅 (28)
In the opening direction, the torque applied on the spring should stay under the sliding limit expressed in Eq. [START_REF] Takaki | Development of a 2-d.o.f. finger using load-sensitive continuously variable transmissions and ultrasonic motors[END_REF].

𝜏 𝑏 (e 2 𝜋 𝑁 𝐴 𝜇 -1) > 𝜏 𝑚𝑎𝑥 𝑖𝑛 1 -𝑅 𝑅 (29)
These three conditions on 𝜇, 𝑁 𝐴 , and 𝑁 𝐵 have to be respected. While the choice of material acts on 𝜇, it stays constrained to common materials (steel, aluminum, bronze to keep the mechanism affordable).

Numerical Application.

In this work a myoelectric hand with high performances (80N, 300mm/s) is considered. Considering kinematics from a tridigital hand as shown on Fig. 1 with an equivalent lever 𝑙 𝑒𝑞 =130mm and assembled with a geared reduction between LAVT and fingers of 1/26, several objectives and constraints have been set:

• a maximal input torque 𝜏 𝑚𝑎𝑥 𝑖𝑛 = 100N.mm given by the motor and the first stages of reduction;

• a minimal transition torque 𝜏 𝑡 𝑜𝑢𝑡 > 15N.mm to overcome the frictions and glove elasticity;

• a maximal output torque 𝜏 𝑚𝑎𝑥 𝑜𝑢𝑡 = 400N.mm needed for the power grasp of 80N;

• a speed reduction at mode switch 𝜔 𝐼 /𝜔 𝐼 𝐼 ≥ 5 to keep sufficient speed while grasping;

• an efficiency at maximal torque 𝜂(𝜏 𝑚𝑎𝑥 𝑜𝑢𝑡 ) > 80%, induced by the last objectives and compatible with the energy optimization goal. 1, where the column "Chosen" specifies the parameters chosen by the designer to meet the specifications, and the other parameters arising from the chosen ones. The material used for spring and frictions surface is steel.

Similarly to Figs. 6 and7, the input to output characteristic and the efficiency coefficient of the three configurations are shown in Fig. 8. 𝑅 is constant in the three configurations, while 𝜏 𝑡 and 𝜏 𝑏 are varying with 𝛿𝑟 𝑎 and 𝛿𝑟 𝑏 . We observe a plateau between mode I and mode II for two of these configurations on Fig. 8 (left), created by a sliding torque 𝜏 𝑏 bigger than the transition torque 𝜏 𝑡 , induced by 𝛿𝑟 𝑎 > 𝛿𝑟 𝑏 . On this plateau, the spring does not slip on surface A nor on surface B, which blocks the mechanism. The efficiency is not defined in this interval, Fig. 8 (right). Using a DC motor as input with a simple voltage control, this interval does not seem to cause any problems. Indeed, while the mechanism will tend to block, the motor output torque will increase rapidly as a response of speed decrease, and pass the interval.

The efficiency is supposed to be maximal (𝜂=1) in Mode I, while there is no sliding of the spring and the others possible frictions are neglected, as shown in Eq. ( 16).

Experimentations

4.1 LAVT Prototype Overview. A first functional prototype has been designed as a proof of concept to validate the theoretical model developed in the last section. The functional parts (spring, friction surfaces, gears) of the prototype are designed at scale for further integration in a prosthesis, but the overall prototype has been designed to be manufactured and assembled easily. The friction ring including surface B and the friction hub including surface A attached to the carrier are changeable to permit experiments with different diameter friction surfaces. The chassis is partially transparent to allow seeing all parts moving. A section view of a CAD and a picture of the prototype are presented in Figs. 9 and 10. As shown on Fig. 11, a constant load torque is applied to the output shaft through a pulley and a predetermined mass 𝑀. The input shaft and its pulley are driven by the experimenter at a constant low speed through a cable and a force sensor, giving the torque applied on the input shaft. The force sensor is a Micro Load Cell (Phidgets CZL616C), and the corresponding signal is amplified and acquired using a PhidgetBridge module. For each output torque given by an output mass 𝑀, the measured input torque is acquired and averaged along several turns to get a mean value of the input torque. A range of masses from 2.0g to 385.0g and two 3D printed pulleys ⌀50mm are used to apply output torques from 0N.mm to 95N.mm. This setup should be consolidated before testing greater torques. However the range chosen is sufficient to show the transition between the two working modes of the LAVT.

Measuring the viscous friction and the efficiency at given speed would be interesting, but requires adapted measurement tools that we do not have access to.

Results.

Figure 12 shows the signal acquired by the force sensor. The load cell has been calibrated before the measurements to compensate the weight of the pulley and taking into account the cable angle. It can be seen on Fig. 12 that the noise in not negligible. However, taking the average value limits the impact of the noise on the measure.

We also observe that a non-constant residual friction torque appears and varies on an entire turn (visible on the Fig. 12 for 𝑀 = 31.5g). It has been noticed that when the spring begins to expand under load before the transition, the spring can touch slightly the outer ring on one side if all parts are not perfectly centered. It creates a residual friction torque.

Figure 13 shows the results of the experiment compared to the theoretical data. A first order interpolation of experimental data is also plotted.

Slip and stick. A slip and stick effect appears in mode II between the spring and the carrier. This effect can be avoided by playing with materials, surface roughness or lubrication.

Screw effect. When the spring is slipping of the carrier in mode II, its helicoidal shape creates a force with tends to stretch itself. While a counter-force from the spring rigidity can limit the spring extension, it can be not sufficient to keep the spring at its right place in the assembly.

"Dead turn". Even if the dynamic behavior of the LAVT is out of the scope of this first analysis, it is interesting to observe that the spring needs to be preloaded before transition when a torque is applied on the output shaft. Thus, when the output shaft is blocked by an object, the input shaft has to turn several turns before actually shift the LAVT to mode II. The number of spring turns before transition Δ𝑁 𝑡 can be calculated through the stiffness of the spring and the number 𝑁 𝑓 of free spires:

Δ𝑁 𝑡 = 𝑁 𝑓 𝑟 𝑛 𝐸 𝐼 𝜏 𝑡 (30)
When the carrier is stopped, the movement of the spring and ring gear will be amplified by the PGT, such as the number of turns Δ𝑁 𝑖𝑛 𝑡 of the input shaft will be larger.

Δ𝑁 𝑖𝑛 𝑡 = 1 -𝑅 𝑅 Δ𝑁 𝑡 = 1 -𝑅 𝑅 𝑁 𝑓 𝑟 𝑛 𝐸 𝐼 𝜏 𝑡 (31)
For 𝑁 𝑓 = 6 in our prototype, we have Δ𝑁 𝑖𝑛 𝑡 = 1.36tr. This "dead turn" can create a delay for the user which has to be taking into account, but also limits the shocks on the motor shaft when the fingers contact an object.

Configurations comparison and discussion. From Tab 2, the configuration 2 seems to be most interesting to use, with the highest maximal output torque 𝜏 𝑚𝑎𝑥 𝑜𝑢𝑡 . The configuration 1 shows the worst performances. These results do not correspond to the expected results of Tab. 1 and Fig. 8, where configuration 1 has the best performances and configuration 2 has the worst.

Tolerances, manufacturing process, surfaces roughness, lubrication and assembly conditions are varying with each configuration, and could explain the differences between theoretical and experimental results. The effects of such changes will have to be investigated in the further studies by repeating measurements in different conditions. In particular, a second prototype with separated PGT and selector clutch could help to identify the friction sources and to test the different configurations of the selector clutch without a complete disassembly of the PGT. The manufacturing precision of the gears and the spring have also to be improved for better performances.

With a better knowledge of the manufacturing tolerances needed in this application, the manufacturing costs could be optimized for a commercialized prosthetic hand.

Additional frictions. From the interpolation, we can easily observe additional frictions. Table 2 shows the friction torques calculated from interpolations. These frictions can easily be explained:

• in mode I, dry frictions can appear from the bearings on the input shaft, the output shaft and the ring gear;

• in mode II, dry frictions can appear from bearings but also from the gears of the PGT which is activated.

Conclusions and Future Works

This paper reports an analysis of the energy consumption for hand prostheses and a step-by-step method to size the transmission mechanism for a given specification for the prostheses. The aim of this project is to provide innovative solutions for accessible prosthetic hand with high performances and low energy consumption.

A prototype has been manufactured and assembled, and the operating principle of the mechanism has been validated theoretically and experimentally. The numerical tests and the experimentation show that the transition torque can be controlled as desired, and that this force amplification system seems to be useful, even with unwanted additional friction.

This mechanism could help designing accessible and powerful prosthetic hands. With a constant energy consumption, using this mechanism can multiply the grasping force by four without changing the speed, or double both speed and grasping force with a constant energy consumption. This feature can offer to the user a more useful prosthesis for daily life activities. This mechanism could be used more generally in all embedded systems that require both speed and force at different times, and where energy efficiency, weight and cost are constrained, such as mobile robots performing grasping tasks.

About perspective this prototype produced could be improved to reduce the residual friction. Indeed, differences between theoretical and experimental results were observed. The effects of parameters not taken into account in the model such as assembly conditions or lubrication are suspected, but further study is needed.

The future work of this project will also consist in writing a dynamic model of the mechanism to take into account the effect of the springs. Secondly, a study of the robustness and fatigue resistance can be carried out. Finally, the integration of this mechanism into a global non-backdrivable transmission will be necessary.

Fig. 1

 1 Fig. 1 Contact points p U , p T and force definition F U /T on a tridigital prosthetic hand

Fig. 2

 2 Fig. 2 LAVT kinematics diagram in mode I when 2 and 3 are locked (no reduction) and mode II when 0 and 3 are locked (reduction)

Fig. 3

 3 Fig. 3 Overrunning clutch using wrap spring clutch, external (left) or internal (right)

Figure 5

 5 introduces the different parts of the planetary gear train and the selector clutch combined together.

Fig. 4 Fig. 5

 45 Fig. 4 Spring contact profile of Selector Clutch

Fig. 7 η

 7 Fig. 7 η as function of τ out at quasi-static state for five different pairs of (R, τ t ), with τ b = τ t

4. 2 7 Fig. 8 Fig. 9

 2789 Fig. 8 τ i n as function of τ out (left) and η as function of τ out (right) of the three selected configurations

Fig. 10

 10 Fig. 10 Picture of LAVT Prototype

Fig. 12 Force

 12 Fig. 12 Force sensor raw data for two different output masses for Configuration 1

Fig. 13 1 Parameter

 131 Fig. 13 Comparison of theoretical and experimental input-output torque characteristic of Configuration 1

Table 1 Sizing results of configuration studied

 1 Three different configurations have been chosen with different dimensions of friction surfaces, in order to test the influence of these dimensions. The results are presented in Table

	Parameters Config. 1 Config. 2 Config. 3 Chosen
	𝜏 𝑚𝑎𝑥 𝑖𝑛	-	100N.mm	-	✓
	𝑅	-	1/5	-	✓
	𝜏 𝑡 𝑖𝑛	17N.mm	17N.mm	19.5Nmm	✓
	𝜏 𝑡	68N.mm	68N.mm	78N.mm
	𝜏 𝑚𝑎𝑥 𝑜𝑢𝑡	432N.mm 418N.mm 418N.mm
	𝜂(𝜏 𝑚𝑎𝑥 𝑜𝑢𝑡 )	86.4%	83.6%	83.6%
	𝜔 𝐼 /𝜔 𝐼 𝐼	-	5	-
	𝑁 𝑠𝑎𝑡	-	3	-	✓
	𝑍 4	-	48	-	✓
	𝑍 3	-	12	-
	𝑍 1	-	18	-
	𝑟 𝑠	-	0.5mm	-
	𝛿𝑟 𝑏	0.5mm	0.5mm	0.575mm	✓
	𝑟 𝑛	-	8.7mm	-
	𝛿𝑟 𝑎	0.5mm	0.6mm	0.6mm	✓
	𝑁 𝐴	-	2	-
	𝑁 𝐵	-	3	-

Table 2 Identification of residual friction losses

 2

	5

Corresponding Author. July 6,

2 https://www.ottobock.fr 3 https://www.steepergroup.com 4 https://www.ossur.com 5 https://www.taskaprosthetics.com 6 https://www.covvi.com 7 https://www.hy5.no 8 https://www.bionitlabs.com

Funding Data

This research was supported by ANRT CIFRE grant n°2019/1721, which funded the first author's doctoral studies.

Conflict of Interest

There are no conflicts of interest.


Ch Person

L Person

E Carre

J Rius

Ph

S Coupez

Toutain

ORIGINAL TECHNIQUES FOR DESIGNING WIDEBAND 3D INTEGRATED COUPLERS

In this paper, we propose some original technological conifigurations for implementing highly coupled -v�ideband structures in a 3D environment. Thanks to a convenient combina tion of thinkable topologies, difficulties com monly encounten:d with a classical approach can be solved. Different design examples of couplers are given, and experimental and simu lated results are presented.

INTRODUCTION

In the last few years, a lot of works have been Therefore, as the constraints are quite differents for each region, specific topologies must be systematically chosen and optimized. Neverthe less, the technological compatibility between each section must be taken into consideration. 2) Hig_h couvling_ level structures ------------------------

1) Low couvling level structures

  published about the design of microwave cou plers, with persisteint preoccupations in terms of bandwidth and coUlpling level possibilities. On one hand, high coupling levels are reachable by means of Lange� structures, or Tandem topo logies; nevertheless, limitations are observed in terms of bandwidth because of synthesis consi derations ( quatenvavelength structures) and electrical perturbations (discontinuities, medium inhomogeneity). On the other hand, reaching wider frequency bandwidth range is generally performed by using cascaded structures. In this case, as the basic considered elements have intrinsic limita tions in terms of reiachable coupling levels, dis continuities and bandwidth, great problems are often encountered. Today, multilevellc�d microstrip topologies be come widespread, then solving problems of high coupling levels ( overlaping process) (1]. .. (5]. Nevertheless, in accordance with in volved materials and considered transmission line topologies, extremely wide operating bandwidths are not thinkable (phase velocity difference >low directivity level). If the "cascaded" solution seems to be the more attractive opportunity for reaching wide bandwidth, a specific work must be done on each basic structure, concerning topologies, dispersion, and discontinuities. In this way, we propose an original design technique, based upon multilayer multitechnology concepts. DESIGN OF ORIGINAL BASIC STRUC TURES FOR MULTISECTION COUPLER When designing multisection couplers, low coupling levels are generally needed for lateral sections while high coupling values are required for the center sections (respectively about 16.SdB and 1.65dB for a 3dB third order O.ldB ripple coupler, for example).

  Classical planar coupled lines can be used to implement low coupling level structu res. However, this will result in a significant spacing between transmission lines, and thus, in a great difference between phase velocities, reducing the directivity of the coupler. To en sure the phase velocities equivalence, we have 1 developed an inverted TFMS (Thi n Film Mi croStrip lines) 16.5dB coupler on alumina substrate, in a multileveled configuration. 1• •. :: : ,, .... .

Fig. 1 :

 1 Fig. 1 : Inverted TFMS 16.15 dB coupler (Center frequency : 1 OGHz) The coupled lines are directly laid down on the substrate (permittivity 9.6), with a 30µm dielectric overlay (permittivity 9.5), and an up per ground plane. The homogeneity of the structure is forced, and the isolation is naturally improved (less than -45dB). This coupler has been implemented and tested on a probe station; indeed, in relation with the line width (less than 50µm), inverted TFMS to CPW (coplanar waveguide) transitions have been implemented at the different ports. Speci fic models have been defined to take into ac count losses and parasitic effects involved by such interconnecting lines. In addition, as a two-port S-parameters extrac tion procedure is employed, the two other ac cesses are terminated by 50 ohms screen-printed CPW loads, which have been characterized (return loss -20dB up to lOGhz, -lOdB above).

Fig. 2 Fig. 2 :

 22 Fig.2 shows the corresponding experi mental results; Note that the 50 ohms CPW loads significantly degrade the return loss and isolation parameters. When all previously des-

  So as to remain compatible with the previous planar coupler (inverted TFMS cou pler), we have investigated new topologies of structures leading to high coupling levels. Fig.3 depictes one basic configuration, based upon the CPW technology in a multilayer medium. High coupling levels are achieved by considering a reentrant CPW topology, the third conductor beeing located on the upper dielectric layer as well as the ground planes; The modelization is performed by means of HP-MDS models, con sidering lateral CPW ground planes as conduc tors with a reduced width.

  'll'z-�f---.,. =-.Eig,A : Ideal simulated [S] parameters Due to th� upper reentrant conductor, this second structure is also less sensitive to technological dispersions, and provides better results in terms of directivity, the main part of the signal beeing concentrated in the dielectric. 3dB couplers have been realized and tested. As mentionned on fig. 5, return loss and isolation are significantly degraded with respect to ideal simulated! ones (fig.4) because of re flection coefficients related to 50 ohms loads.

Fig. 5 :

 5 Fig.5 : 3dB multileveled reentrant CPW coupler Measurement (-) I Simulation with parasitic effects(---) When parasitic effects specific to test conditions are taken into account (fig.5), simu lation and experiment become close to each other; the 3dB reentrant CPW coupler is ob viously correctly defined and gives performance similar to the ideal expected ones (fig4)3) Wideband high couvling_ level couvlers

Fig. 6 :

 6 Fig. 6 : 3dB multisections coupler -description The upper TFMS ground plane for la teral 16. 1 SdB sections is used in order to reject parasitic modes potentially generated by the center CPW structure; here, no bounding opera tion is required thanks to this configuration.0.0

Figure 7 :

 7 Figure 7 : Multisections 3dB coupler : simulation


Christophe Calvez
email: christophe.calvez@telecom-bretagne.eu

Christian Person

Jean-Philippe P Coupez

François Gallée

Romain Pilard
email: romain.pilard@st.com

Frédéric Gianesello

Ezzeddine Hilal

Daniel Gloria

Didier Belot

R Pilard #

F Gianesello #

D Gloria #

D Belot #

H Ezzeddine

Miniaturized hybrid antenna combining Si and IPD technologies for 60 GHz WLAN applications

Keywords: millimeterwave, hybrid antenna, System in Package, silicon substrate, IPD™ technology. I

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INTRODUCTION

At millimeter wave frequencies, high data rate applications such as Wireless HDMI require low cost and low power System on Chip (SoC) for addressing mass-market products and expectations. Thanks to the recent progress of Integrated Circuits (ICs) on CMOS or BiCMOS Silicon technologies, the complete integration of the RF front-end on a single chip is now achievable [START_REF] Scott | A Silicon 60-GHz Receiver and Transmitter Chipset for Broadband Communications[END_REF]. Furthermore, due to the small operating wavelengths considered (e.g. 5 mm in air @ 60GHz), a higher integration level can be ensured by co-integrating the antenna. Besides quite a high gain value (14dBi) is expected for Wireless HDMI applications compliant with the different established standards (ECMA, 802.15.3c [2], WirelessHD, WiGig Alliance). This application requires beamforming capabilities to prevent multipath effects generated by human presence. The use of antenna array is necessary for respecting these specifications. Due to the Silicon (Si) substrate characteristics (dielectric constant, loss tangent, thickness), integrated antennas exhibit quite low gain and reduced radiating efficiency [START_REF] Pinto | 79Ghz Integrated Antenna on Low Resistivity Si BiCMOS exploiting above-IC processing[END_REF][START_REF] Pilard | Folded-slot Integrated Antenna Array for Millimeter-Wave CMOS Applications on Standard HR SOI Silicon Substrate[END_REF]. In addition, the implementation of antenna array on Si is not appropriate because of the high insertion losses of planar distributing network on Si as well as corresponding huge dimensions with respect to acceptable chip size (cost motivations). Thus, a hybrid integration technique appears as a good trade-off to report radiation elements and lossless feeding structures on an appropriate passive circuit supporting material, like glass substrate or fused silica [START_REF] Zwick | Broadband Planar Superstrate Antenna for Integrated Millimeterwave Transceivers[END_REF][START_REF] Liu | A Patch Array Antenna for 60 GHz Package Applications[END_REF].

II. IPD™ TECHNOLOGY

In this paper, we propose to use the IPD™ (Integrated Passive Devices) technology from STMicroelectronics for the antenna substrate because it is suitable for antenna integration at millimeter wave frequencies due to its high quality factor (low dielectric constant and loss tangent) and its low production cost. The question lies therefore in the excitation of this antenna array and especially in the perfect control of the interconnections between integrated on chip excitation ports and antenna array input ports. If low gain completely integrated transceiver can be reasonably imagined on Si, as a single onchip antenna can be used, higher directivity modules would require antenna array, and thus non-acceptable dimensions for being completely integrated. In addition, note that the packaging of such transceiver has to be simultaneously taken into consideration, as the packaging usually significantly contributes to the global cost of integrated modules, especially in the mmWave frequency range (alignment, loss and higher order modes spurious suppression constraints)

Consequently, the antenna array on IPD™ can be also considered as the upper part of the transceiver package, then minimizing cost thanks to its active contribution to the module performances. The interconnection between the Si chip and the array substrate becomes a fundamental parameter in the design and the optimization of such RF structures. Impedance matching, insertion losses and spurious mode excitations must be considered as challenging issues. In the literature [START_REF] Felic | Flip-Chip Interconnection Effects on 60-GHz Microstrip Antenna Performance[END_REF][START_REF] Zhang | Antenna-in-Package Design for Wirebond Interconnection to Highly Integrated 60-GHz Radios[END_REF], flip chip techniques use bonding wires or bumps with compensation network to reduce interconnection losses.

In a previous work [START_REF] Calvez | New millimeter Wave Packaged Antenna Array on IPD Technology[END_REF], we have presented an antenna array designed on IPD™ technology, mounted on the Si chip supporting excitation sources by means of μ-bumps (h = 100 μm). In this paper, we focus on the minimization of interconnection losses by exploiting coupling possibilities between an upper patch antenna reported on inverted glass substrate, and coupling slot directly integrated on Silicon, i.e. at the power amplifier (PA) output or at the low noise amplifier 1 (LNA) input (Fig. 1). This can be considered as an additional benefit of the proposed hybrid integration technique. The challenge of the hybrid integration is the interconnection between the ICs chip and the antenna part. The different proposed interconnection solutions generate insertion losses or impedance mismatches. So, we propose an alternative approach where the antenna is electromagnetically excited by a coupling slot directly implemented on the Si-chip. The radiating patch is implemented on the bottom face of the IPD™ material and the coupling slot is located on the M6 metallization layer of the BiCMOS B9MW technology (Fig. 2). The glass substrate (εr=4.6 -h=300μm) is also flip chipped by bumps on the silicon chip. The air gap located between the slot dipole and the patch is related to the bumps height (height=100μm after assembly). The advantage of this solution is the compatibility between the propagation mode (CPW: coplanar waveguide) at PA output and dipole excitation. The ground of the CPW transmission lines and the coupling slot is assumed as the ground plane of the patch. Besides, the input slot impedance can be modified according to the PA output or LNA input impedance. Therefore, the antenna is perfectly inserted in this equivalent package, and ready to be optimally interfaced with active elements.

A first design of the coupling slot integrated on a BiCMOS process (Low Resistivity (LR) Si -12

.cm) from STMicroelectronics is proposed hereafter. The non-resonating slot is excited with a 50 ohms CPW line (W=30μm -G=9μm) and its dimensions are as follow: length L slot =966μm -width W slot =20μm. The slot is centered under the upper patch and is optimized in order to have the optimal magnetic coupling with the upper square patch (length L patch =1.65mm -width W patch =1.65mm). The proposed antenna is presented on Fig. A first simulation on HFSS™ with taking into account μbumps leads to a 30dB return loss at 60 GHz, and a 8% relative bandwidth @ VSWR=2 (57.4-62.2 GHz) (Fig. 4). This antenna presents a gain of 5 dBi and a F/B ratio of 17.5 dB at 60 GHz (Fig. 5). We obtain 55° and 66° half-power beamwidths for the E and H planes, respectively. The mounting of this antenna is on-going and matching and radiation measurement results will be presented at the conference.

IV. ALUMINA-IPD™ ANTENNA FOR PROCESS VALIDATION

A preliminary study has been leaded to validate this concept exploiting Lab-STICC internal technology: replacing the silicon substrate by alumina substrate for the excitation structure, and glass substrate (IPD™ technology) by Rogers™ substrate for the patch antenna. This choice is justified by the relative similarity of these supports (electrical characteristics quite similar). A comparative characterization procedure has been realized from Lab-STICC and STMicroelectronics test benches [START_REF] Calvez | Packaged hybrid Si-IPD™ antenna for 60 GHz applications[END_REF]. After the concept validation and characterization steps, the flip-chip technique has been validated with the realization of a hybrid antenna combining alumina substrate and IPD™ technology (Fig. 6). The air cavity located between the coupling slot and the patch depends on the μ-bumps diameter and reception pads dimensions implemented on alumina and glass substrates. In our case, a 100 μm air cavity height is obtained from a 140 μm μ-bumps diameter. The reception pads permit to achieve a high quality chip report with a perfect alignment. The return loss measurement of this antenna presents a very good agreement with simulation and confirms the assembly process quality (Fig. 7). A 25 dB matching is measured at 59.9 GHz with a 5% relative bandwidth @ VSWR=2. This antenna presents a simulated gain of 6.6 dBi and a F/B ratio of 13 dB at 60 GHz (Fig. 8). The radiation measurements will be presented at the conference.

V. CONCLUSION

A self-packaged antenna solution for 60 GHz communications is presented. The advantage of this antenna is mainly related to its excitation structure directly implemented on BiCMOS B9MW technology, thus allowing immediate interfacing with On-Chip ICs for beamforming and/or array weighting operations. The combination of low cost IPD™ technology allows a perfect integration of a low cost antenna solution in package. The elementary antenna achieves a simulated gain of 5 dBi at 60 GHz, and exhibits a 8% relative bandwidth. This antenna is being currently manufactured with the BiCMOS B9MW and IPD™ technology from STMicroelectronics -Crolles and Tours (France), respectively. The measurements results of this antenna will be presented during the conference. A preliminary antenna has been realized based on alumina and glass substrates. The measurements results present a good agreement with simulation and confirm the high quality of the flip-chip assembly process.

In order to increase gain and with respect to standard specifications for mmWave applications (Wireless HDMI), the hybrid Si-IPD™ antenna appears as a convenient solution for array implementation thanks to the limited dimensions of the patch element reported on a low cost substrate.

Figure 1 .

 1 Figure 1. Side view of the mmWave package with the Si-IPD™ packaged antenna

Figure 2 .

 2 Figure 2. Side view of the Si-IPD™ packaged antenna.

3

 3

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Figure 3 .

 3 Figure 3. Top view (a) and 3-D view (b) of the Si-IPD™ packaged antenna.

Figure 4 .

 4 Figure 4. Simulated return loss of the Si-IPD antenna.

Figure 5 .

 5 Figure 5. Simulated radiations patterns at 60 GHz: E (blue) and H (red) plane.

Figure 6 .

 6 Figure 6. Photo of the Alumina-IPD antenna.

Figure 7 .

 7 Figure 7. Measured and simulated return loss of the Alumina-IPD antenna.

Figure 8 .

 8 Figure 8. Simulated radiation patterns at 60 GHz: E (blue) and H (red) plane.

ACKNOWLEDGMENT

This work is supported by the collaborative MEDEA+ European project "Qstream".