HUMAN ADAPTABLE VARIABLE STIFFNESS SPRINGS

Various examples of systems, methods, and applications of variable stiffness springs are described. In one example, a variable stiffness joint apparatus can include a torsional spring; a variable stiffness mechanism comprising a self-locking mechanism and a linkage system, the self-locking mechanism comprising an auxiliary spring; and an actuator in communication with the auxiliary spring of the self-locking mechanism. When the actuator changes position, a force is applied to the auxiliary spring by the actuator and a stiffness is adjusted at an energy cost that is independent of the stiffness of the spring and the energy stored by the spring. In another example, a self-adjusting variable stiffness mechanism can include a compression spring. The energy stored by compressing the compression spring and the mechanism can self-adjust a stiffness to enable energy accumulation using a same maximal compression force which is not dependent on the energy accumulated in the spring.

BACKGROUND

A conventional spring has constant stiffness that defines how much force it exerts upon deflection and how much energy it stores upon deflection. The stiffness of a spring depends on the material, shape, and size of the spring. Variable stiffness springs change their shape or size to increase or decrease stiffness; provide more or less force and store more or less energy upon the same deflection.

DETAILED DESCRIPTION

In the context described above, various examples of systems, methods, and applications of a human adaptable variable stiffness springs are disclosed herein. In a non-limiting example, a variable stiffness spring apparatus can have a control device to allow a user to select a stiffness modulation without using precisely timed forces. For example, a variable stiffness joint apparatus is described where the stiffness of the joint can be changed by the human similar to manually changing gears in bicycles. In another non-limiting example, a variable stiffness spring apparatus can ensure that energy is accumulated in the spring after repeated compression of the spring. For example, a self-adjusting variable stiffness apparatus is described where the stiffness of the apparatus is changed automatically similar to the automatic gear shifting in cars.

Described below are various embodiments of the present systems and methods for human adaptable variable stiffness springs therefor. Although particular embodiments are described, those embodiments are only exemplary implementations of the system and method. One skilled in the art will recognize other embodiments are possible. All such embodiments are intended to fall within the scope of this disclosure. Moreover, all references cited herein are intended to be and are hereby incorporated by reference into this disclosure as if fully set forth herein. While the disclosure will now be described in reference to the above drawings, there is no intent to limit it to the embodiment or embodiments disclosed herein. On the contrary, the intent is to cover all alternatives, modifications, and equivalents included within the spirit and scope of the disclosure.

The following examples are put forth to provide those of ordinary skill in the art with a complete disclosure and description of how to construct and use the systems and methods disclosed and claimed herein. Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, etc.), but some errors and deviations should be accounted for.

It is to be understood that, unless otherwise indicated, the present disclosure is not limited to particular materials, manufacturing processes, or the like, as such can vary. It is also to be understood that the terminology used herein is to describe particular embodiments only and is not intended to be limiting. It is also possible in the present disclosure that steps can be executed in different sequences where this is logically possible.

In the following discussion, a general description of the systems of the present disclosure and their components is provided, followed by a discussion of the operation of the same. Non-limiting examples of human adaptable variable stiffness springs are discussed.

A conventional spring has constant stiffness that defines how much force it exerts upon deflection and how much energy it stores upon deflection. The stiffness of a spring depends on the material, shape, and size of the spring. Variable stiffness springs change their shape or size to increase or decrease stiffness, provide more or less force, and store more or less energy upon the same deflection.

Variable stiffness springs can be used as transmission mechanisms similar to the variable gear transmission in bicycles and cars. The benefit of variable stiffness spring transmission compared to variable gear transmission is that the former enables power amplification (or de-amplification), while the latter cannot provide power amplification (or de-amplification).

To demonstrate the power amplification capability of a variable stiffness spring, it is assumed that the spring is initially compressed by a motor, human limb, or any other force, such that it stores E Joules of energy. The average power of the spring is defined as, p=E/T, the ratio between the energy stored by the spring and the time T required by the spring to fully extend and release the stored energy. The time required by the spring to release the stored energy depends on the stiffness of the spring k because a spring with lower stiffness will need more time to fully extend compared to a spring with higher stiffness: k1<k2implies T1>T2(assuming that both springs are attached to the same mass). This example shows why and how variable stiffness springs can amplify power: k1<k2implies p1<p2.

Power amplification (and de-amplification) is a beneficial feature of a transmission mechanism because power amplification (and de-amplification) can be used to achieve rapid acceleration (and breaking). For example, power amplification (and de-amplification) can be used to increase the productivity of an industrial robot, by speeding up (or slowing down) the robot performing a pick-and-place task. Also, power amplification can be used to speed up (or slow down) a robot exoskeleton assisting or augmenting human limbs in jumping, walking, running, swimming, or other everyday activities.

However, increasing the stiffness of a variable stiffness spring can cost a large amount of energy. For example, the minimum amount of energy needed to increase the energy stored by a linear helical spring k1<k2is the elastic potential energy added to the spring while changing the spring stiffness:

While this formula suggests that increasing spring stiffness upon the same deflection will cost energy proportional to the energy stored by the spring ΔE˜E1, it also shows that the stiffness of the spring could be changed at a low energy cost when the spring stores no energy E1=0.

The reasoning above has led to prior designs of variable stiffness springs that afford low energy cost stiffness variation when the spring stores no energy.

Disclosed herein is a simple control method that leverages this feature in the context of human assistance during walking with a variable stiffness hip joint. The method has the benefit of only requiring a small control force to change the stiffness of a variable stiffness spring because it changes stiffness when the spring stores no energy E1=0 (when the variable stiffness joint is undeflected). However, in many applications, condition E1=0 can only be met at isolated time points during oscillatory motion, and therefore, the method has a practical limitation of requiring precisely timed control forces when the spring stores no energy or when it stores a limited amount of energy E1≈0.

The requirement for precisely timed control forces imposes a limitation on the practical realization of low energy cost stiffness modulation in variable stiffness springs. For example, it imposes a limitation on the practical realization of a variable stiffness spring with human changeable stiffness.

Variable stiffness springs with human changeable stiffness are springs where the stiffness change is done by an effortless finger, hand, arm, or limb movement. Variable stiffness springs with human changeable stiffness are similar to the variable gear transmission mechanism used in bicycles and cars, as the latter afford gear shifting with not only small force but also a slow finger or limb motion.

To address the limitation of using precisely timed forces for low energy cost stiffness modulation, a novel variable stiffness spring is disclosed. The key element of the design is the series spring directly connected to the variable mechanical advantage mechanism that changes stiffness. The series spring affords a small force to vary the stiffness of the spring to be generated at any time during the motion, for example, the time when the spring stores energy during oscillatory motion. In this way, the series spring removes the requirement of a precisely timed force to enable low energy cost stiffness variation.

An example embodiment and a use case of the series elastic spring-driven variable stiffness spring is described herein. The series spring can be used to convert previously designed variable stiffness springs into a variable stiffness spring that affords stiffness variation using small and imprecisely timed forces. The series spring is not limited to devices where that stiffness is varied by a human; it can be used in variable stiffness springs where the stiffness is varied by a motor. In the latter case, the series spring changes the requirement of a weak and fast motor to a weak and slow motor; a motor that has a lower peak power requirement.

The benefit of a variable stiffness spring transmission compared to variable gear transmission is that the former enables power amplification (or de-amplification), while the latter cannot provide power amplification (or de-amplification). The human adaptable variable stiffness springs requirement for precisely timed control forces imposes a limitation on the practical realization of low energy cost stiffness modulation in variable stiffness springs. For example, it imposes a limitation on the practical realization of a variable stiffness spring with human changeable stiffness. Variable stiffness springs with human changeable stiffness are springs where the stiffness is changed by an effortless finger, hand, arm, or limb movement. Variable stiffness springs with human changeable stiffness are similar to the variable gear transmission mechanism used in bicycles and cars, as the latter afford gear shifting with not only small force but also a slow finger or limb motion.

Turning toFIGS.1A and1B, shown are an isometric view of an example human-selectable variable stiffness spring apparatus100(FIG.1A) and a section view (FIG.1B). The human-selectable variable stiffness spring apparatus100can include a torsional variable stiffness spring102and a self-locking pivot point mechanism104. For example, the torsional variable stiffness spring102can be a spiral torsion spring (also referred to as a torsional spring, torsional joint spring, or joint spring herein). The torsional variable stiffness spring102can be mounted about a shaft106. The human-selectable variable stiffness spring apparatus100can also include a linkage system108arranged to contact the torsional spring102and change a stiffness of the torsional spring102. The human-selectable variable stiffness spring apparatus100also includes an actuator110. The self-locking pivot point mechanism104is suitable to be incrementally controlled by the actuator110.

The torsional variable stiffness spring102can include a spiral torsion spring102. In an example, the torsional variable stiffness spring102can be a 3D printed carbon fiber reinforced spiral torsion spring102due to customizability and large volumetric energy density. The spiral torsion spring102can be fabricated using Onyx (nylon filled with chopped carbon fiber) with half of the layers reinforced with continuous strands of carbon fiber. The self-locking pivot-point mechanism104and linkage system108can be used to vary the mechanical advantage of the spiral spring over the joint.

The self-locking pivot point mechanism104can include a ratchet-pawl mechanism that includes a linear ratchet112and a pawl114. The self-locking pivot point mechanism104can also include a pawl support116and an auxiliary spring118(also referred to as a series spring herein). The linear ratchet112can be arranged orthogonal to and offset from the shaft106. The linear ratchet112and pawl support116can be coupled to a housing120, where the linear ratchet112is stationary and the pawl support116can translate along housing supports122that are arranged parallel to the linear ratchet112. The housing120can also include a mounting plate124from which the shaft106extends and a means to connect the housing supports122to the mounting plate124. The pawl114coupled to the pawl support116at a pivot point126and configured to engage with the linear ratchet112. The pawl114can engage with the linear ratchet112and pivot about the pivot point126to translate along the linear ratchet112.

The self-locking pivot point mechanism104also includes a pawl-release spring130(also referred to as a parallel spring herein). The pawl-release spring disengages the pawl from the ratchet. The pawl-release spring130is attached to the pawl114at an offset to the pivot point126and connected to the pawl support116. The auxiliary spring118and pawl-release spring130are positioned at an offset from a pivot point126of the pawl114such that the auxiliary spring118and pawl-release spring130generate opposing moments on the pawl114. Together, the auxiliary spring118and pawl-release spring130can control the engagement of the pawl114with the linear ratchet112to enable the user to change the stiffness of the torsional spring102.

The auxiliary spring118is coupled in series between the actuator110and the pawl114. A user can control the actuator110via a connected control device128suitable for manual control of the actuator110. The user can select to increase or decrease the stiffness of the torsional variable stiffness spring102without precise timing. A level of stiffness of the torsional variable stiffness spring102based at least in part on a position of the pawl114with respect to the linear ratchet112. When the actuator110changes position, a force is applied to the auxiliary spring118by the actuator. For example, the actuator110can comprise a Bowden cable146extending from a manual control device128(FIG.3), which will be described in further detail. When a user extends or retracts the actuator (or cable)110, a force and a moment are generated via the auxiliary spring118to pivot the pawl114about the pivot point126to engage or disengage the pawl114from the linear ratchet112. When an applied force of the actuator110, and the force generated by the auxiliary spring118is larger than the force of the pawl-release spring130and the reaction force of the joint spring102, the pawl114is moved to increase the stiffness of the torsional spring102. When an applied force of the actuator110, and the force generated by the auxiliary spring118is smaller than the force of the pawl-release spring130and the reaction force of the joint spring102, the pawl114is moved to decrease the stiffness of the torsional spring102. While a cable is shown as the actuator110in an example, other types of actuators can be relied on to displace the auxiliary spring118.

The linkage system108can be arranged between the torsional variable stiffness spring102and the self-locking pivot point mechanism104to modulate the stiffness of the torsional spring102. The linkage system108can include a lever arm132having a slot134, a first linkage arm136, and a second linkage arm138. The first linkage arm136is rotatable about shaft106and pivotably coupled by a first pin140to a first end portion of the lever arm132. The second linkage arm138is rotatable about shaft106and can contact the torsional spring102. The distal end of the second linkage arm138can have a second pin142at a distal portion of the second linkage arm138that is arranged to slide within slot134of the lever arm132. The pawl support116can have a support pin144that extends from a surface opposite along the same axis of the pivot point126which supports the pawl114. The lever arm132can be arranged such that the support pin144of the pawl support116of the self-locking pivot point mechanism104is positioned within the slot134of the lever arm132. The lever arm132is positioned to pivot about the same axis as the pivot point126of the self-locking pivot point mechanism104and to vary the mechanical advantage of the spiral spring102.

As shown inFIGS.2A and3, the variable stiffness joint apparatus100can include a control device128suitable for manual control of the actuator110by a user. For example, the actuator110of the control device can include a Bowden cable146. The control device128can include at least one lever148to modulate stiffness by moving the actuator110. The control device128can be handheld and operable by a finger of the user, requiring only a small force by the user. The user can incrementally select the stiffness via the at least one lever148. In some examples, the control device128can have a first lever148ato increment stiffness and a second lever148bto decrement stiffness. In some examples, the control device128can have an index indicator150to display a value to indicate a level of stiffness. Although a Bowden cable146and handheld control device128are shown as an example, other configurations and implementations of user-controlled actuators can be relied on.

The method of changing the stiffness of a torsional variable stiffness spring102can include applying a force to the auxiliary spring118of a self-locking pivot point mechanism104. The force can be applied by the actuator110to provide a positive or negative force on the auxiliary spring118. Applying a force to an auxiliary spring118of a self-locking pivot point mechanism104can include changing a position of the actuator110that acts on the auxiliary spring. In an example, the actuator110can be controlled by a user applying small forces via a handheld control device128. For example, when a user extends or retracts the actuator110, a force and a moment are generated via the auxiliary spring118to pivot the pawl114about the pivot point126to disengage the pawl114from the linear ratchet112. When an applied force of the actuator110, and the corresponding moment generated by the auxiliary spring118about the pivot point126is larger than the moment generated by the pawl release spring130, and the force generated by the auxiliary spring118is larger than the reaction force applied by the joint spring102to the support pin144, the pawl114translates along the linear ratchet112to increase the stiffness of the torsional spring102. When an applied force of the actuator110, and the corresponding moment generated by the auxiliary spring118about the pivot point126is smaller than the moment generated by the pawl release spring130, and the force generated by the auxiliary spring118is smaller than the reaction force applied by the joint spring102to the support pin144, the pawl114translates along the linear ratchet112to decrease the stiffness of the torsional spring102.

The self-locking pivot point mechanism104is coupled to the torsional variable stiffness spring102via the linkage system108. Changing a position of the pivot point126of the self-locking pivot point mechanism104is based at least in part on the force applied to the auxiliary spring118which can cause the stiffness of the variable stiffness spring to change.

Examples of the design of human-selectable variable stiffness spring apparatuses100are discussed in further detail below. For example, variable stiffness springs with human-selectable stiffness can be used as a human-adjustable variable stiffness joint. The stiffness is adjusted at an energy cost that is independent of the stiffness of the spring and the energy stored in the spring. The stiffness can be adjusted without large or precisely timed forces provided by a motor or human.

Springs are commonly used in wearable robotic devices to provide assistive joint torque without the need for motors and batteries. However, different tasks (such as walking or running) and different users (such as athletes with strong legs or the elderly with weak legs) necessitate different assistive joint torques, and therefore, springs with different stiffness. Variable stiffness springs are a special class of springs which can exert more or less torque upon the same deflection, provided that the user is able to change the stiffness of the spring. Presented herein is a novel variable stiffness spring design in which the user can select a preferred spring stiffness similar to switching gears on a bicycle. A leg-swing experiment demonstrates that the user can increment and decrement spring stiffness in a large range to effectively assist the hip joint during leg oscillations. Variable stiffness springs with human-selectable stiffness could be key components of wearable devices which augment locomotion tasks, such as walking, running, and swimming.

Mechanical springs are commonly used in wearable devices to provide assistive torque without the use of motors and batteries. Prior works have shown that unpowered spring-driven exoskeletons can reduce the metabolic cost of walking by 7% and running by 8%; in both cases, a fixed stiffness spring was optimized across users. Alternatively, a variable stiffness spring with selectable stiffness could enable users to choose the most optimal spring stiffness for the task, similar to how a bicycle derailleur enables cyclists to select the most optimal gear ratio independent of the cyclist and the cycling speed.

Variable stiffness springs have been previously used in lower limb prostheses and orthoses to help humans with motions such as walking, running, and stair-ascent. Many of the previously designed variable stiffness springs ensure that a small force can be used to adjust the spring stiffness when the spring is unloaded. However, for oscillatory motions such as the swing of the hip during walking, running, or swimming, the spring may only be at equilibrium for a fraction of a second during each cycle of the motion. Consequently, if the human aims to effortlessly change stiffness during an oscillatory task, then the human must precisely apply the force to change stiffness when the spring is not deflected at each cycle.

Using a variable stiffness robot actuator, a small but fast motor can change spring stiffness during oscillatory motion, once each motion cycle, by applying precisely timed forces. Replacing the motor with a human limb and a bicycle hand shifter is impractical because the user would be required to operate the hand shifter at precise times. However, by placing a spring in series between the hand shifter and the mechanism which adjusts spring stiffness, the requirement for precisely timed movements can be eliminated. The variable stiffness spring with human-selectable stiffness replaces a weak but fast motor with a human finger to control the stiffness.

The variable stiffness mechanism described herein enables the human to change the stiffness of the spring in the same way the derailleur enables cyclists to change the gear ratio of the bicycle. The device consists of a 3D-printed composite spiral spring and a variable stiffness mechanism. The stiffness of the spring is changed by a series-spring actuated Bowden cable hand shifter, and a unique self-locking mechanism implemented with a linear ratchet and pawl. The device allows the user to effectively change the assistance provided to the user in a leg swing experiment, where the hip joint of the human is augmented with the variable stiffness spring. The user can also increment and decrement the spring stiffness using a bicycle hand shifter, the same way a cyclist would down-shift or up-shift the gear ratio to adapt to different terrains and speeds while riding the bicycle.

Model—Human-Driven Variable Stiffness Spring Joint

The model of the human-driven variable stiffness spring joint is shown inFIG.2A. For example, the variable stiffness spring with human-selectable stiffness100comprises the hand shifter128, series spring118, and the self-locking variable stiffness mechanism which includes a self-locking pivot point mechanism104and the linkage system108. The joint is composed of a spring102and a mechanism that changes the stiffness of the spring. The free-body diagram of the model is a schematic representation of the variable stiffness spring shown inFIG.2B.

The torque-angle relation of the variable stiffness spring, as shown inFIG.2B, is defined by:

where τ is the joint torque, θ is the joint angle, k is the joint stiffness, while x denotes the position of the pivot point126.

The joint stiffness k(x) depends on the design of the mechanism. The stiffness of the torsional spring102, shown inFIG.2A, is given by the following relation:

where ksis the constant stiffness of the torsional spring attached to the joint, d is the length of the first linkage arm136attached to the shaft, while l is the length of the second linkage arm138attached to the spring102. According to (1.2), the stiffness of the joint is a monotonically increasing function of the position of the pivot point126, x.

Changing the position of the pivot point126changes the mechanical advantage of the spring102over the joint. The equation governing the motion of the pivot point is given by:

where m is the mass of the stiffness modulating mechanism, f is the external force applied to modulate joint stiffness, while F is the reaction force of the spring aiming to move the pivot point126by back-driving the stiffness modulating mechanism (seeFIG.2B). The latter effect appears because the spring always tends to move the pivot-point to the position associated with the lowest joint stiffness.

In order to prevent the reaction force of the spring102from changing the position of the pivot point126, a spring-loaded linear ratchet-pawl mechanism112,114(FIG.2A) is used. The mechanism locks when the force required to move the pivot point f exceeds the threshold locking force f0of the spring-loaded pawl; it is unlocked otherwise.

When the ratchet-pawl mechanism112,114is locked, the reaction force of the joint spring102cannot move the pivot point126in the direction that lowers the joint stiffness,

but the externally applied force f can be used to move the pivot point and increase the joint stiffness, given that the externally applied force is larger than the reaction force of the spring, f>F(θ, x) in (1.3).

When the ratchet-pawl mechanism112,114is unlocked 0<f<f0, the reaction force of the spring can be used to lower the joint stiffness under the following condition 0<f<f0<F(θ, x) in (1.3). This condition will be satisfied when the spring is considerably deflected, as in that case, the reaction force of the spring is much larger than the threshold force f0used to lock the ratchet-pawl mechanism112,114.

Working Principle

The physical requirements to change the joint stiffness using small forces are examined below.

A variable stiffness joint placed at the human hip and attached to the leg is considered. It is further assumed that the leg swings back and forth with frequency ω, and amplitude θmax, in walking or running,

To increase the joint stiffness, an external force f that is larger than the spring force opposing the motion of the pivot point is applied,

This condition can be satisfied by an arbitrarily small force f, when the spring is un-deflected, θ=0, or a small force when the spring is slightly deflected, θ≈0.

It is assumed that the force provided by the human is limited,

and using (1.5) and (1.6), the time available to change the stiffness of the joint using the maximal force that can be provided by the human can be estimated by

where T=2π/ω is the period of leg oscillations.

Relation (1.8) suggests that if the maximal force to change the spring stiffness fmaxis small compared to the maximal reaction force of the spring Fmax, then the time window in which the joint stiffness can be changed Δt is also small:

Therefore, the timing of the external force f must be precise in order to increase the spring stiffness with a small force.

The requirement for precise timing is circumvented in our device by using a spring between the hand shifter and the pivot point, seeFIG.2A(series spring).

In a typical work cycle, the human would actuate the hand shifter once or multiple times in order to reduce the length of the Bowden cable, and consequently extend the series spring of stiffness ks, until the maximum force is reached,

If the ratchet-pawl mechanism112,114is unlocked, then extending the spring will move the pivot point and increase the joint stiffness. If the ratchet-pawl mechanism112,114is locked, extending the spring will increase the force in the series spring but will not move the pivot point or increase the joint stiffness. Since the series spring can be extended while the ratchet-pawl mechanism is locked (1.6), the human can use the hand shifter over nearly the whole period of oscillations T, except perhaps the short time window Δt when the ratchet-pawl mechanism112,114unlocks and the series spring118moves the pivot point126to increase the joint stiffness.

Consequently, the time available for the human to apply force is not limited to Δt, and is largely independent of the force applied by the human.

In summary, the series spring removes the precise timing requirement to change the joint stiffness using small forces. The series spring also enables the user to extend the spring over multiple oscillation cycles, which further mitigates the precise timing required to change the joint stiffness without the series spring (1.9), or the time available to change stiffness during a single cycle with the series spring (1.11).

In the example shown inFIGS.1A and1B, the torsional variable stiffness spring102can be a 3D printed carbon fiber reinforced spiral torsion spring102due to customizability and large volumetric energy density. The spiral torsion spring102can be fabricated using Onyx (nylon filled with chopped carbon fiber) with half of the layers reinforced with continuous strands of carbon fiber. For example, the carbon fiber spring can have an estimated stiffness of ks≈24 Nm/rad. The adjustable pivot-point linkage mechanism104can be used to vary the mechanical advantage of the spiral spring over the joint.

InFIG.4, experimental results of measured torque-angle data is shown. A static deflection experiment was performed to estimate the torque-deflection behavior of the variable stiffness joint. During the experiment, the spring was deflected at six different stiffness configurations.

The joint is characterized by the following torsional stiffness values,

This stiffness enables the spring to provide ±[3, 36] Nm assistive joint torque at ±30 deg joint rotation, which amounts to around 35% of the average human hip torque for a 75 kg person during walking at normal speeds (1.6 m/s).

One example of a control device128comprises a hand shifter (FIG.3). The hand shifter128and the locking mechanism104can be used to change the stiffness and hold the torque provided by the torsional spring102. The hand shifter has two levers that, when pressed, either extend or retract the Bowden cable. In an example, the combined mass of the hand shifter128and Bowden cable146is about 0.3 kg. The Bowden cable is a steel cable routed inside a flexible housing. In the bicycle, the Bowden cable shifts the chain between different sets of sprockets.

Bowden cables have been extensively used in wearable devices to transfer force. In our device, the two ends of the Bowden cable are fastened to the hand shifter and the series spring, while the series spring is connected to the pawl which can rotate about the pivot point, as shown inFIG.1A. By changing the length of the Bowden cable, the human generates a force and a moment about the pivot point. The moment generated about the pivot point disengages the pawl from the ratchet, such that the force can move the pivot point. In this way, using the hand shifter and the Bowden cable, the human can change the stiffness of the joint.

In the human-selectable variable stiffness spring apparatus100, the pivot point self-locks through the use of a linear ratchet-pawl mechanism112,114, shown inFIGS.5A and5B. The mechanism which changes stiffness includes a linear ratchet rack112, a pawl114, a series spring118between the pawl114and the Bowden cable146, and a parallel spring130between the pawl114and the pivot-point housing120. The pawl114engages with the ratchet112to prevent the motion of the pivot point126when the large spiral spring102is loaded. The series spring118and parallel spring130of stiffness ksand kp(seeFIG.5B) control the engagement of the pawl114to enable the user to change the stiffness of the joint.

To increase stiffness, the user generates a force on the Bowden cable146, which deflects the series spring118. When the large spiral spring102is un-deflected, the series spring118pulls the pawl114and consequently translates the pivot point126(seeFIG.5B-right). The stiffness of the series spring ks≈6000 N/m is chosen small enough such that the user can extend it, but large enough such that it can move the pivot point when the large spiral spring is unloaded.

To decrease stiffness, the user extends the Bowden cable146, which causes the cable to slack. When the cable slacks, the series spring118becomes unloaded, which allows the parallel spring130to disengage the pawl114. In this case, the force imposed by the large deflected spiral spring102can move the pivot point, to reduce the joint stiffness, until the slack of the Bowden cable146is removed and the pawl114is re-engaged (FIG.5B—left). The stiffness of the parallel spring130kp≈485 N/m has been chosen large enough to disengage the pawl114around zero joint deflection and small enough to allow the series spring118to re-engage the pawl114upon a small joint deflection.

The human-selectable variable stiffness spring joint is used to augment the human hip joint (shown inFIG.6A) in a leg swing experiment. The purpose of the experiment is to validate the working principle of the device which enables the human to quickly change joint stiffness over a large range during continuous oscillations.

To verify the function of the device, a desk-mounted setup is used, where the variable stiffness spring joint can be attached to the leg of a human, as shown inFIG.6A. The leg of the subject was fastened to the spring using a 3D-printed clamp, while the clamp was connected to the joint using a lever arm. The lever arm features a rotary joint and a prismatic joint such that the leg is not constrained to move in the lateral and longitudinal directions while being attached to the joint.

The hip angle θ was captured using a rotary magnetic encoder. The position of the pivot point x was measured using a linear magnetic encoder. The torque provided by the variable stiffness joint was estimated using the measured joint angle θ, the measured pivot point position x, and the experimental torque-deflection curves shown inFIG.4.

A simple exploratory experiment was performed, where the subject was asked to (i) swing one leg continuously back and forth at a comfortable frequency and a relatively constant amplitude of ±20 degrees, (ii) fully increment the bicycle shifter until the maximum stiffness has been reached, and subsequently, (iii) fully decrement the shifter until the minimum stiffness was reached. The protocol was approved by the Institutional Review Board of Vanderbilt University Medical Center (N220192).

The experimental data is shown inFIG.6C. The mechanism is shown inFIG.6Bwhile the joint stiffness was incremented (top) and decremented (bottom). The angle of the hip joint is shown inFIG.6C(top). The position of the pivot point is shown inFIG.6C(middle). The joint torque is shown inFIG.6C(bottom).

FIG.6Bshows snapshots of the device during the experiment with the corresponding timestamps labeled inFIG.6C. The left snapshot shows an example of a stiffness increment where the series spring is first extended while the leg is away from equilibrium; in this case, the mechanism is locked, and subsequently, the series spring pulls the pivot point to a higher stiffness configuration when the leg is around equilibrium (FIG.6B—top). The top snapshot shows an example of a stiffness decrement where the Bowden cable is slacked and the parallel spring lifts the pawl until the pivot point moves to a lower stiffness configuration and the slack of the Bowden cable is removed (FIG.6B—bottom).

FIG.6C(top) shows the joint angle during the experiment. The subject was able to generate continuous oscillatory leg motion such that the amplitude of the joint angle was around ±20 degrees.

FIG.6C(middle) shows the position of the pivot point, and therefore the joint stiffness, during the experiment. The stiffness was increased from the minimum value (shifter index 1, where k(x)≈6 Nm/rad) to the maximum value (shifter index 10, where k(x)≈70 Nm/rad) during the oscillatory motion. The position of the pivot point oscillates approximately ±2 mm for each stiffness configuration. This oscillation was caused by the return spring which by default disengages the pawl in order to decrement stiffness as described herein. The oscillations did not cause detrimental effects during the experiment.

FIG.6C(bottom) shows the estimated joint torque of the device during the experiment. As the user increased the joint stiffness of the spring, the torque of the spring was also increased from 1 Nm to around 20 Nm.

In summary, the experiment demonstrated that (i) the locking mechanism was able to successfully hold a given joint stiffness configuration as the device generated 1-20 Nm joint torque, and (ii) the user was able to effectively use the hand shifter to increment and decrement joint stiffness in a relatively large range of 6-70 Nm/rad, during continuous swings. The results show that the proposed device enables the human to adapt joint stiffness using an intuitive interface provided by the hand shifter of the bicycle.

A novel human-adjustable variable stiffness joint is described in which the user can select different joint stiffness, similar to cyclists selecting different gear ratios on a bicycle. The device enables the human to use small and non-precisely timed forces to change joint stiffness, rather than requiring the user to provide large forces or small but precisely timed forces. The ability of the human-adjustable variable stiffness joint to maintain and change stiffness during continuous oscillatory motion is also shown.

Customization of robot exoskeleton assistance for different users, tasks, and speeds has been shown to reduce metabolic demand in walking and running and may be useful for other everyday tasks. Individualized joint stiffness values could provide benefits to users across different speeds of walking. Individualized joint stiffness values may also help improve joint motion patterns and correct a reduced joint motion range of users with impairment. Finally, individualized joint stiffness values may be used to better augment users performing physically demanding tasks, such as lifting, jumping, running, or walking with a heavy load.

Human-adjustable variable stiffness joints can be key components of mechanically adaptive robot exoskeletons where different users can choose between different levels of assistance for different locomotion tasks.

Energy Accumulation Under Force and Deformation Constraints

In another example, the above concepts can be extended and adapted to different scenarios. As a non-limiting example, a variable stiffness joint apparatus can be an uncontrolled mechanical device or mechanical automaton. The stiffness of a spring can be changed automatically with a kinematics design of a mechanism to ensure that energy is accumulated in the spring after repeated compression of the spring. As will be described in more detail, the self-adjusting variable stiffness mechanism can accumulate an increased amount of energy upon repeated compression with a constant maximal force, whereas a regular spring can only accumulate more energy by increasing the maximal compression force. Consequently, in the self-adjusting variable stiffness mechanism, each stroke can have the same maximal force, such that repeated spring compression does not require a larger force for each new stroke. In a non-limiting example, a device or apparatus using iterative energy accumulation as described herein can be a device wearable by a user, such as an exoskeleton, where repetitive actions allow for energy accumulation. However, the concepts can be relied upon for other devices that do not require direct human interaction. For example, the device or apparatus can be relied upon for other configurations and applications. In another non-limiting example, the concepts can be applied to tools or as part of a transmission mechanism attached to a motor to drive heavy machinery by first accumulating energy with a small torque-limited motor and then releasing the accumulated energy to generate significant force beyond what would be possible using the same motor.

Springs can provide force at zero net energy cost by recycling negative mechanical work to benefit motor-driven robots or spring-augmented humans. However, humans have limited force and range of motion, and motors have a limited ability to produce force. These limits constrain how much energy a conventional spring can store and, consequently, how much assistance a spring can provide. An approach to accumulating negative work in assistive springs over several motion cycles is discussed. By utilizing a novel floating spring mechanism, the weight of a human or robot can be used to iteratively increase spring compression, irrespective of the potential energy stored by the spring. Decoupling the force required to compress a spring from the energy stored by a spring could enable spring-driven robots and humans to perform physically demanding tasks without the use of large actuators.

Springs can enable robots actuated by motors and humans “actuated by muscles” to perform physically demanding tasks with reduced force requirements from the actuators. Typically, a spring is compressed slowly over a longer period of time, while the energy stored by the spring is released rapidly. In this way, the spring provides power amplification beyond what a motor-driven robot or “muscle-actuated” human can do without the assistance of a spring. However, the energy stored by a spring is limited by the maximum force used to compress the spring. Consequently, the maximal force that a robot or human can generate limits the amount of energy a spring can store, and the level of assistive benefit a spring can provide. This limitation may be alleviated by leveraging the energy storage ability of springs over multiple loading and unloading cycles instead of a single cycle.

In mechanical resonance, the benefit of springs is leveraged over multiple cycles of energy storage and release, instead of a single cycle. A familiar example is a pogo-stick, essentially a spring in series with the human legs, that allows the user to jump repeatedly to accumulate energy and reach jump heights much greater than in a single jump. To accomplish such a feat, the pogo-stick relies on iteratively increasing the kinetic energy of the human through multiple jumps. This increase in kinetic energy is required to generate large contact forces to compress the pogo-stick spring and thereby increase the energy stored by the spring. However, large forces are challenging for humans and robots to generate without increasing their kinetic energy.

A method and a device for iteratively accumulating energy using only the static gravitational force provided by the mass of a spring-driven robot or the mass of a human augmented with a spring leg exoskeleton are described. The method utilizes the repeated application of a constant static force that is independent of the energy stored by the spring. The method also relies on a new device, which belongs to the class of floating spring mechanisms. The device is an energetically passive variable stiffness spring which automatically adjusts its stiffness to ensure that a constant force can compress the spring regardless of how much energy is stored by the spring.

For example, a self-adjusting variable stiffness mechanism can include a compression spring, where energy is stored by compressing the compression spring and the mechanism self-adjusts a stiffness to enable energy accumulation using a same maximal compression force which is not dependent on the energy accumulated in the spring. Further, repeated compressions increase an amount of energy stored.

InFIG.7, an example of a self-adjusting variable stiffness mechanism200is shown as a model of a lower-limb variable stiffness spring exoskeleton attached parallel to the legs of a user. The self-adjusting variable stiffness mechanism200can include a leg structure202and a floating spring assembly204. The leg structure202can include first and second linear shafts206,208coupled by a hinge joint212. The floating spring assembly204can include a compression spring214. The first and second ends216,218of the floating spring assembly204can be slidably attached to the first and second linear shafts206,208, respectively. In this example, the first linear shaft206can have a free end220that can coincide with the hip (H) of a user, and the second linear shaft208can have a free end222that can coincide with the ankle (A) of a user. The first and second linear shafts206,208can be configured such that the hinge joint212coincides with the knee (K) of the user. As shown in this example, the first and second linear shafts206,208, illustrated as leg segmentsHKandKA, can be equal in length and the spring214is assumed to remain vertical (x is constant) as the leg deforms by Δl. While shown in this example as a model of a user-worn device, the concepts can be relied upon in other configurations and applications.

Energy Accumulation Using Springs

In an example, a simple energy accumulation task is considered, where the human is augmented with a spring exoskeleton attached parallel to the legs. In this task, the user compresses the spring by repeatedly squatting with the exoskeleton. The energy stored by the spring is retained by locking the spring at the bottom of each squat. As the human returns to the standing height, the spring shifts to a new configuration that grants the user a greater mechanical advantage over the spring for the next iteration. The greater mechanical advantage ensures the user can compress the spring at the beginning of each squat cycle until a desired amount of energy is accumulated in the spring. In the described iterative energy accumulation process, the force required by the human to achieve full spring compression is independent of the energy stored by the spring.

Shown inFIGS.8A-8Cis an example of repeated compression of a self-adjusting variable stiffness mechanism200. As illustrated, an example squatting task using a simple spring-mass model of the human augmented with a conceptual lower-limb variable stiffness spring exoskeleton is shown. In this example, the relationship of the spring assembly204to the leg structure202is shown for select body positions of the user during repeated compressions. InFIG.8A, in the first stage of spring compression the endpoints of the spring assembly304are fixed while the user compresses the spring214with a squat. InFIG.8B, the endpoints of the spring are free while the spring is locked. The mechanical advantage of the user over the spring is increased as the user stands and the spring shifts towards the knee joint. InFIG.8C, the user can iteratively increase the energy stored by the spring214.

The human and the spring-leg exoskeleton are abstracted into a basic model shown inFIG.9A. The human augmented with a lower limb exoskeleton is shown as a mass-spring system. The leg deformation is described as Δl. The body mass is supported by a spring with stiffness knand deformed length sn±; where the superscripts ± denote the pre-squat and post-squat spring lengths, respectively, and the subscript n denotes the number of squats performed during repeated squatting.

A single squat, starting from an upright standing position and ending at the fully squatted position is considered. Due to the geometric constraint of the leg, the leg deformation during a squat is given by

Because the human leg can push but cannot pull against the ground while squatting, the force exerted by the leg on the center of mass must be positive,

Finally, it is assumed that the human legs can produce enough force to stand up after each squat without the support of the exoskeleton. Any leg force that can overcome the weight of the human F≥mg suffices this assumption.

An example of the human leg force that enables squatting from a standing position to an equilibrium squat position is shown inFIG.9B. The example force-deflection of the human leg is shown with the solid line that leads to an average leg force

shown with the dashed line. The maximum amount of energy accumulated during one squat E1 maxis shown in the shaded area.

At standing the human limbs fully support the mass such that F=mg and the spring-leg exoskeleton does not provide any force. In the fully squatted position, the human limbs may support the mass with a force F ∈ [0, mg) while the spring leg provides the rest of the force required to keep the center of mass in static equilibrium,

At the bottom of the squat, the energy stored by the spring leg depends on the human limb force. Assuming an average limb forceF, the energy stored by the spring is given by:

In order to simultaneously satisfy (2.3) and (2.4), the average force of the human legFduring the squat must satisfy the following condition:

According to (2.4) and (2.5), the maximum amount of energy that can be stored in the spring during a single squat is given by:

Relation (2.6) directly shows that the amount of energy accumulated in the spring is restricted by the range of motion and the limited gravitational force available to compress the spring.

Increasing the energy accumulated in the spring beyond the maximum amount of energy that can be stored in the spring during a single squat may be done by multiple squats. However, there are three main practical challenges to accumulating energy via multiple squats. First, the mechanism must provide increased mechanical advantage to compress the spring, such that the same force can be used to compress the spring even as the spring stores more energy. Second, the mechanism must provide controllable coupling between the spring and the leg, such that the same leg deformation can be used to input energy into the spring in subsequent squats independent of how much energy is stored by the spring. Third, to ensure efficient energy accumulation, the two prior tasks should be accomplished while maintaining the energy stored in the spring between subsequent iterations.

In the example shown inFIG.7, the spring maintains a vertical orientation but shifts towards or away from the knee joint to change the mechanical advantage of the human over the spring. Consequently, the self-adjusting variable stiffness mechanismalters mechanical advantage by controlling the endpoints of the spring while the spring is locked, which maintains the potential energy stored by the spring. In turn, this ability to control the endpoints of the spring allows the leg deformation to be decoupled from the spring deformation, independent of the energy stored by the spring.

Model—Cyclic Energy Accumulation

FIG.7shows the floating spring variable stiffness leg for a single squat iteration. In the leg, points H, K, and A coincide with the user's hip, knee, and ankle, respectively. The thigh and shank segments HK and KA are assumed to be of equal length lt. The spring is also assumed to maintain its vertical orientation independent of the leg deformation. In the mechanism, the length of the spring s is defined by leg length l and the position of the spring x,

while the force required at the hip F1to compress the spring is defined by,

where s0is the uncompressed length of the spring and ksis the stiffness of the spring.

These relations suggest that by moving the spring towards the knee joint—decreasing x—a small constant force F1could be used at the hip to compress the spring despite a potentially large spring force Fs, and consequently, the large amount of energy stored by the spring.

As a result, the mechanism shown inFIG.7could accumulate a large amount of energy when compressed by the weight of the human over multiple squats. In order to predict the behavior of the mechanism beyond a single squat, the simple example of a human performing a repetitive squat task to accumulate energy in the spring is considered as shown inFIGS.8A-8C.

First, similar to (2.3), it is assumed that the spring-leg supports the weight of the user at the end of each squat,

To define the spring length at the end of the squat sn+, the spring location xnmust be related to the spring length at the beginning of the squat sn−. The simple relation below follows from locking the spring length between the end of the previous squat and the beginning of the next squat (FIGS.8A-8C),

According to (2.10), the energy stored by the spring will be retained between squats,

Finally, using (2.7) and (2.10), a recurrence relation that predicts the position of the spring across squat iterations is defined:

Substituting (2.9), (2.10), and (2.12) into (2.8), it is found that the force required to compress the spring at the beginning of the next squat is always lower than the constant gravitational force available to compress the spring,

FIG.10Ashows the force-deflection predicted during multiple squats, during which the maximal force provided by the human is bounded by the weight of the user. This force is compared to the force required to achieve the same spring deformation in a single squat (dashed line). Further, the vertical dashed lines show that the spring deformation is maintained between iterations, as required by (2.10).

FIG.10Bshows the energy accumulation process for the iterative method (gray), with energetic potential normalized by the maximum energy that can be achieved in a single squat provided by the weight of the user, E1 max, as defined in (2.6). The four squats shown the minimum number of repeated squats to achieve the maximum spring deformation shown inFIG.10B.

The spring accumulates the same amount of energy through four squats (gray) than in a single squat (gray dashed) but with less than half of the required force (FIGS.10A and10B). Furthermore, the reduction in force translates to over five times more stored energy as compared to what can be accumulated in a single squat subject to the same maximum force (FIG.10B). Following the repeated squats, the spring can be reset to the initial mechanical advantage, x=lt, where the accumulated energy can be released to provide double the assistive force as compared to the maximal force used to compress the spring (FIG.10A) and supply significantly more energy than what is stored by the spring when compressed with the maximal force in a single squat (FIG.10B). The new functionality could allow a user to accumulate energy for lifting a large load, or enable a spring-driven robot to accumulate energy for increasing jump height.

Turning toFIG.11, an example implementation of a self-adjusting variable stiffness mechanism300is shown. The self-adjusting variable stiffness mechanism300includes the same features as the self-adjusting variable stiffness mechanism200and is described in further detail. Although the self-adjusting variable stiffness mechanism300is shown in an experimental setup, the features and concepts can be relied upon for other configurations and implementations, such as the exoskeleton discussed in relation toFIGS.7-9.

As shown inFIG.11, the self-adjusting variable stiffness mechanism300is shown in an experimental set-up. The self-adjusting variable stiffness mechanism300can include a leg structure302and a floating spring assembly304. The leg structure302can include first and second linear shafts306,308coupled by a joint pin310to form a hinge joint312. The floating spring assembly304can include a compression spring314. The first and second ends316,318of the floating spring assembly304can be slidably attached to the first and second linear shafts306,308, respectively. In this example, the first linear shaft306can have a free end320connected to a load cell324. For example, similar to the hip inFIG.7, the free end320of the floating spring assembly304can be compressed and the force measured by the load cell324. The second linear shaft208can have a free end322that is shown as fixed in this example. The self-adjusting variable stiffness mechanism300also includes first and second unidirectional pulleys326,328mounted in coincidence with the joint pin310. The first and second unidirectional pulleys326,328can be configured to move the ends316,318of the floating spring assembly304in unison.

The compression spring314in the floating spring assembly304can be compressed repeatedly to store energy. The floating spring assembly304can also include a piston330, a cylinder332, and a lock334. The energy stored by the compression spring314is retained by locking the floating spring assembly304. Lock334secures the compression spring314axially. In a non-limiting example, as shown inFIG.11, the lock334can include a shoulder bolt friction clamp335that passes orthogonally through a hole (not shown) in the piston330. For example, cylinder332can include flat sides as an interface for the shoulder bolt335which are suitable to allow continuous locking of the spring314. Although a shoulder bolt is shown as an example, other non-friction-based locking devices or friction-based locking devices can be relied upon to allow continuous locking of the spring.

The first and second unidirectional pulleys326,328can include the first and second double drums336,338. The first and second double drums336,338can be mounted in coincidence with the joint pin310. Each of the first and second double drums336,338are suitable to hold two cables340,342each, such that each pulley326,328has separate cables wrapped in opposing directions. For example, for the first linear shaft306, a first cable340aconnects to an extension spring344athat provides a torque on the pulley326, while a second cable342ais connected to an end320of the floating spring assembly304. Similarly, for the second linear shaft308, a first cable340bconnects to an extension spring344bthat provides a torque on the pulley328, while a second cable342bis connected to the other end322of the floating spring assembly304.

The leg structure302can also include a ratchet346and a pawl348at each of the first and second unidirectional pulleys326,328suitable to lock rotation of each unidirectional pulley326,328with respect to a pulley bracket (FIGS.12A-12E). Each end of the floating spring assembly304can also include a linear ball bearing350(FIG.11—bottom) in both ends320,322that allow the floating spring assembly304to slide freely along the respective linear shafts306,308.

While the non-limiting example shown inFIG.11is one implementation, the structure can be relied on in other configurations and implementations. For example, the self-adjusting variable stiffness mechanism300can include means to secure the self-adjusting variable stiffness mechanism300to a leg of a user such that the hinge joint coincides with the knee of the user, one end of the first linear shaft320coincides with a hip of the user, one end322of the second linear shaft308coincides with the ankle of a user. In another example, a hand tool may include the self-adjusting variable stiffness mechanism300. In yet another example, the self-adjusting variable stiffness mechanism300can be part of a transmission mechanism attached to a motor to drive heavy machinery by first accumulating energy with a small torque-limited motor and then releasing the accumulated energy to generate significant force beyond what would be possible using the same motor.

The method of energy accumulation using the self-adjusting variable stiffness mechanism300includes compressing the compression spring314housed in a floating spring assembly304to incrementally store energy. Energetic potential is normalized by a maximum energy that can be achieved in a single compression using the same maximal compression force. The method also includes repeatedly compressing the compression spring314and locking a length (l) of the floating spring assembly304between the end of one compression and the beginning of the next compression. The length (l) of the floating spring assembly304is defined by the distance between the two ends of the spring320,322. The energy stored by the compression spring314is retained between compressions. The floating spring assembly304is slidably attached to the first and second linear shafts306,308and can lock to the compressed length between compressions. A force required to compress the compression spring314at the beginning of a repeated compression is lower than a constant gravitational force. In an example, a wearable exoskeleton can include the floating spring assembly and be suitable to be worn on a leg of a user. In the example of an exoskeleton, the compressing of the compression spring can include the user squatting.

As described above,FIG.11depicts the spring-leg apparatus designed for the proposed energy accumulation task. The device includes three major sub-assemblies: the leg structure, the compression spring, and the spring retraction mechanism.

First, the leg structure302is formed by two linear shafts306,308connected by brackets at the knee and pinned to create a hinge joint312. The other ends320,322of each shaft form the hip and ankle of the mechanism, as inFIG.7.

Second, a compression spring314is housed in a piston-cylinder assembly (also referred to as the floating spring assembly herein)304where each end316,318of the assembly connects to a linear ball bearing350a,350bthat slides freely along the leg shafts306,308. In this example, to lock the spring axially, a shoulder bolt335passes orthogonally through a hole in the piston330and rides in a slot in cylinder332, as shown inFIG.11(top). The cylinder features flat sides as an interface for the shoulder bolt335, allowing continuous locking of the spring.

Finally, two unidirectional pulleys326,328, each comprising two drums336,338, are mounted in coincidence with the knee joint pin310, as shown inFIG.11(bottom). One pulley is keyed to the knee pin, while the other pulley spins freely on the knee pin. Both, however, can spin freely with respect to the knee brackets. The double drums336,338on each pulley326,328feature separate cables340,342wrapped in opposing directions. One cable340a,340bconnects to an extension spring344a,344bthat provides a torque on the pulley326,328, while the other cable342a,342bis connected to an end320,322of the spring assembly304. The system of pulleys serves to automatically shift the position of the spring assembly304while maintaining its orientation by balancing the forces of the two retraction springs344a,344b.Consequently, the mechanical advantage between the spring314and the leg is changed between each compression cycle.

FIGS.12A-12Eshow the working principle of the apparatus of compressing the spring and changing the mechanical advantage of the leg over the spring314with the variable stiffness floating spring mechanism.FIG.12Ashows the CAD model of the apparatus300where the respective parts are labeled to help distinguish components responsible for the different endpoints of the spring assembly304. Each leg segment utilizes a pulley326,328and dual cable assembly342,344to move the endpoints350of the spring assembly304in unison.

During compression, seeFIGS.12B and12C, the spring314is unlocked and applies force on the bearing-mounted endpoints350of the spring assembly304. Subsequently, the ratchet346and pawl348lock the rotation of each pulley326,328with respect to their associated knee bracket. This cable-pulley setup then locks the position of the endpoints320,322against the force of the spring. During compression, the endpoints320,322of the spring are fixed along the leg segments306,308by locking the rotation of each respective pulley326,328via a ratchet346and pawl348.

Following the spring compression, the spring314is locked, and the pre-loaded retraction springs344a,344bapply a torque on their respective pulleys326,328, seeFIGS.12D and12E. To change the mechanical advantage, the mechanism extends back to its initial configuration with the spring314locked, allowing the pre-loaded retraction springs344a,344bto rotate each pulley326,328and simultaneously retract the spring endpoints320,322towards the hinge joint312, which may coincide with a knee. Since the ratchet346and pawl348ensure the pulleys326,328can only rotate in one direction, the torque on the pulley from the retraction spring344tends to pull the endpoints320,322of the spring assembly304towards the knee joint312. Therefore, as the mechanism returns to an initial configuration, the tension in the cables automatically shifts the endpoints of the spring toward the knee for a change in mechanical advantage before the next iteration.

Experimental Validation

The apparatus300, shown inFIG.11, was mounted on a mechanical breadboard via a linear rail. The ends of each leg segment306,308were connected to lockable carriages. One carriage was locked in place, acting as the ankle joint fixing the foot of the mechanism to the ground, while the other carriage could move freely along the rail like the hip joint. A load cell (MLP-50, Transducer Techniques) was mounted to a flat plate on the free-moving carriage to measure the force at the hip joint.FIG.13(top) shows the apparatus300in an uncompressed spring314.

First, with the spring314unlocked, a force was applied manually to the load cell on the free slider until a pre-defined maximal force was reached, as shown inFIG.13(middle). At that point, the force was measured by the load cell. While manually applying force does not achieve constant static force during compression, the maximum applied force was held constant to represent the force boundary discussed above.

After collecting the force data, spring314was locked axially by tightening the friction clamp335, and the length of the spring314was measured. Next, the slider was unlocked and moved back to its initial position, as shown inFIG.13(bottom). As described inFIGS.12D and12E, moving the slider shifted the spring assembly304to a new configuration that granted a greater mechanical advantage over the spring314. The process described here was then repeated until maximum spring deformation was achieved.

FIGS.14A and14Bdisplay the experimental result of the validation.FIG.14A, shows the force-deflection trend predicted. Force is observed to increase up to the maximum force, then decrease to allow another squat despite the increased potential energy stored by the spring. The decrease in force required to enable a new squat is accomplished by the ratchet, pawl, and pulley assembly. The iterative force-deflection behavior (solid lines) is compared to the force required to reach the same spring deflection in a single squat (dashed line).

FIG.14Bshows the iterative increase in spring potential. The results show that the spring accumulates the same amount of energy in three squats (solid lines) as compared to that accumulated in one squat (dashed line). However, similar to what was predicted by the model, the mechanism reduces the maximal force necessary to accumulate the same amount of potential energy. In particular, the 25% decrease in maximal force observed inFIG.14Aresulted in 75% more energy accumulated by the spring compared to the energy one could store after a single squat when using the same maximal force. This result follows the same trend observed inFIGS.10A and10B. Further, when the device is reset to the initial mechanical advantage x=lt, it yields nearly 25% more assistive force (FIG.14A) and 75% more energy compared to the maximum force used to repetitively compress the spring and the associated energy stored by the spring when compressed by the maximum force in a single squat (FIG.14B).

While the experimental results were similar to the theoretical predictions, there were notable differences. For example, the mechanism exhibited roughly84percent efficiency, due to the energy loss observed during the experiment. This energy loss is shown inFIG.14Aby the black dashed lines not being vertical between iterations. The loss of energy can also be observed inFIG.14B, where the energy accumulated in the spring first decreased at the beginning of each new energy accumulation cycle.

Two main factors contributed to the observed energy loss; first, the cables used to couple the retraction springs to the spring assembly were not completely inextensible, and second, the ratchet and pawl only provide discrete locking positions of the spring endpoints along the leg shafts and therefore introduced some amount of backlash.

One can also observe inFIG.14Athat force is not initially zero, seeFIG.14B. This initial force was due to the pre-loading of the compression spring to mitigate slack in the pulleys and cables. Also, the forces created by the retraction springs tend to pull the spring endpoints toward the knee, which in turn creates a moment about the knee that wants to straighten the leg.

In summary, a model of a lower-limb spring-leg exoskeleton is disclosed that may allow the human to perform a repetitive squat-to-stand task to accumulate energy. The squat-to-stand task was used as an example of iterative energy accumulation in a spring under force and deformation constraints. A variable stiffness floating spring leg mechanism is used to demonstrate the novel force-deflection and energy storage behavior that allows energy accumulation by repeated compression of the spring despite the same maximal force used in each compression cycle. Our theoretical predictions were experimentally validated using a variable stiffness floating spring mechanism.

The self-adjusting variable stiffness mechanism enables automatic adjustment of the mechanical advantage of the human or a robot over a spring between compression iterations. The mechanism demonstrated that a static gravitational force, provided by the mass of a human or robot, can be used to accumulate energy in a spring independent of the desired amount of energy stored by the spring. The self-adjusting variable stiffness mechanism and the associated energy accumulation method can be applied to implementations that include exoskeletons and spring-driven robots.

The new capability of iterative energy accumulation using a limited static force, could allow humans and robots with limited force capability and limited range of motion to perform physically demanding tasks, for example, to jump higher, move faster, or lift heavier objects, by harnessing the energy stored in assistive springs. The concepts can be relied upon for additional designs of robot exoskeletons and spring-driven robots with enhanced energy storage capabilities.

The above-described examples of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Variations and modifications can be made without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.