Advancements in computational musculoskeletal biomechanics are constrained by a lack of experimental measurement under real-time physiological loading conditions. This paper presents the design, configuration, capabilities, accuracy, and repeatability of The University of Texas at El Paso Joint Load Simulator (UTJLS) by testing four cadaver knee specimens with 47 real-time tests including heel and toe squat maneuvers with and without musculotendon forces. The UTJLS is a musculoskeletal simulator consisting of two robotic manipulators and eight musculotendon actuators. Sensors include eight tension load cells, two force/torque systems, nine absolute encoders, and eight incremental encoders. A custom control system determines command output for position, force, and hybrid control and collects data at 2000 Hz. Controller configuration performed forward-dynamic control for all knee degrees-of-freedom (DOFs) except knee flexion. Actuator placement and specimen potting techniques uniquely replicate muscle paths. Accuracy and repeatability standard deviations across specimen during squat simulations were equal or less than 8 N and 5 N for musculotendon actuators, 30 N and 13 N for ground reaction forces (GRFs), and 4.4 N·m and 1.9 N·m for ground reaction moments. The UTJLS is the first of its design type. Controller flexibility and physical design support axis constraints to match traditional testing rigs, absolute motion, and synchronous real-time simulation of multiplanar kinematics, GRFs, and musculotendon forces. System DOFs, range of motion, and speed support future testing of faster maneuvers, various joints, and kinetic chains of two connected joints.

## Introduction

Joint diseases and disorders, either due to aging or injury, are among the most prevalent, debilitating, and painful medical conditions [16]. Although tremendous advances have been made in musculoskeletal biomechanics, potential breakthroughs are hindered by limitations in acquiring reliable in vivo measurements such as joint contact forces and soft tissue deformations [7,8]. While hip and knee joint contact forces have been measured using instrumented implants [911], these devices are typically implanted in older patients, and the motions collected are limited to relatively slow motions such as gait, stair climbing, and slow jogging. In addition, the behavior may not be representative of what happens in a native joint since geometries and material properties have been altered.

To circumvent these critical barriers related to in vivo studies, investigators have developed computational models and in vitro simulators, the latter to perform measurements on cadaveric specimens. Computational models are very versatile since virtually any type of tissue can be simulated, in parallel to applying a variety of kinematic and kinetic conditions. The main drawback of predictive computational modeling is the need for thorough validation, which in turn relies on experimental measurements. Bates et al. [12] identified 77 anterior cruciate ligament (ACL)-related in vitro studies from 2004 to 2013, which may be categorized as robotic or mechanical impact tests.

Numerous robotic simulators [1321] have been developed to replicate the complexity of in vivo joint biomechanics. Many simulations are static or quasi-static [1315,19,22], but some have applied time-varying kinetics and kinematics to more accurately apply physiological loading conditions [1618,20,21,23,24]. The physiological accuracy of in vitro testing is dependent upon numerous factors. Critical to recreating in vivo conditions is the synchronous application of multiplanar joint kinematics, external forces (e.g., ground reaction forces (GRFs) and body weight), and musculotendon forces. In addition, to obtaining realistic joint loading conditions, muscle moment arms must also be replicated.

In particular, musculotendon force control varies tremendously between existing in vitro simulators: nonexistent musculotendon loading [14,15,17,19,21,22], grouped knee flexor and extensor musculotendon loading [16,20,24], and individual musculotendon force control [13,18,25]. Since each individual musculotendon crossing a specific joint uniquely contributes to its stability and therefore internal loading condition [26], grouping individual muscle forces or failing to represent muscle forces altogether can negatively influence the joint kinematics and introduce measurement errors regarding contact forces, ligament strains, and relative joint movement. Musculotendon force application is also affected by muscle moment arms. Since joint kinematics are governed by optimized muscle forces balanced between agonist and antagonist muscles, differences in muscle moment arms will alter these precisely tuned loading patterns and thus any further measurements performed.

Few simulators attempt to apply multiplanar kinematics and kinetics. Full constraint of a single joint requires control of six degrees-of-freedom (DOFs), where a knee consists of a tibiofemoral and a patellofemoral joint. Many simulators limit control to sagittal DOFs [13,15,16,20] and do not fully constrain tibiofemoral DOFs as demonstrated by other simulators [14,1719,2123].

Current methods of reproducing high strain rate loads lack accurate and repeatable control [12]. The recommended solution to this problem is highly dynamic load introduced through precise robotic manipulation [12]. Cassidy et al. [16] demonstrated high-speed loading but only did so with sagittal DOFs and grouped muscles.

To address the current limitations of existing in vitro simulators with the aim of providing improved physiological experimental data, we sought to develop a versatile in vitro multi-joint simulator capable of replicating highly dynamic activities such as running, jump landing, and cutting. As a critical step toward this goal, this paper introduces The University of Texas at El Paso Joint Load Simulator (UTJLS) and includes an outline of the design, a demonstration of its current configuration, and an assessment of its accuracy and repeatability during real-time squat simulations. From this thorough assessment of simulator performance, opportunities are identified for continued advancements toward simulation of highly dynamic physiological loads, variable joints, and kinetic chain testing.

## Materials and Methods

A custom, multiplane simulator was developed with the range of motion (ROM) and component specifications to support variable joint and kinetic chain testing at high speeds. The associated controller functions on a real-time operating system and is reconfigurable to support a wide ROM and a variety of human joints. The performance evaluation provided in this study determined the standard deviations of controller accuracy across four specimens during four squat loading conditions, trial repeatability across four specimens, and specimen repeatability for repeated loading of the same maneuver on the same specimen.

### Component Design.

The University of Texas at El Paso Joint Load Simulator requirements were determined through analysis of lower extremity kinematics and kinetics during highly dynamic maneuvers including cutting, braking, and drop jumping. These maneuvers are of clinical relevance as they commonly lead to injury and account for some of the highest accelerations and forces occurring in the human body. Subject kinematic and kinetic data for this analysis were collected during preliminary tests using in-house motion capture and verified through literature [2729].

Two 6DOF manipulators were designed into the UTJLS, but the three translations of the lower gantry system were not implemented for this particular study (Fig. 1(a)). For this knee study and for validation with literature, the UTJLS manipulators were configured as surrogate hip and ankle joints, accommodating a full-length lower limb. Components of the simulator include various servomotor types (Table 1), tension load cells (Table 2), multi-axis load cells (Table 3), encoders (Table 4), control computers, data-acquisition boards, supplementary electronics, and a custom specimen-mounting fixture.

#### Linear Actuators.

The current configuration applies relative linear motion through the hip gantry system. The required ROMs were determined through compiling the maximum displacements of a subject's hip during the foot-to-floor contact phases of the previously mentioned maneuvers. Each of the three translation axes utilizes two linear servomotors (RIPPED series, Parker Hannifin Corp., Cleveland, OH) guided by linear bearings (Table 1). These motors have a high power density, an electrical time constant of 3 ms, and no backlash. This selection provides the capacity and loading rate that is necessary to follow real-time position and force profiles.

For the purpose of safety, each axis is equipped with emergency stops (SNALD, Enertrols, Farmington Hills, MI) that can be positioned to limit system ROM and is equipped pneumatic brakes (RB15, Nexen Group, Inc., Vadnais Heights, MN) operated by three-way solenoid valves (S8, Pneumadyne, Inc., Plymouth, MN). Both the brakes and solenoid valves are spring loaded and engage in less than 0.12 s.

#### Rotational Actuators.

Each manipulator contains three rotational axes mounted in series with one another. The upper rotations are mounted on a gantry system, while the lower rotations are mounted on a steel stand centered in the upper manipulators' horizontal ROM (Fig. 1(a)). Each rotational axis is driven by a servomotor (MPP series, Parker Hannifan Corp., Cleveland, OH) driving a gearbox (AB series, Apex Dynamics, Ronkonkoma, NY) (Table 1). On each manipulator, the outermost rotation is oriented along the simulator's X-axis with the innermost rotation aligned with the respective bone's mechanical axis (Fig. 1).

#### Musculotendon Actuators.

Accurate application of joint moments from musculotendon forces requires both accurate force magnitude and moment arms, which are dependent upon multiple factors including insertion sites and muscle path [31]. To retain anatomical insertion sites, musculotendon actuators are connected directly to the cadaver tendon. In the case of a knee joint, while muscle insertions on the femur, tibia, and fibula are specimen-specific, surrogate muscle insertions on the pelvis and calcaneus are simulator-specific, i.e., determined by musculotendon actuator placement and steel cable guides. To represent accurate anatomical muscle insertions, the mounting location of each actuator was derived from previously published three-dimensional models (Fig. 2) [32].

The UTJLS has eight musculotendon actuators configured to replicate the following muscles: vastus medialis (VM), vastus lateralis (VL), rectus femoris (RF), semitendinosus (ST), semimembranosus (SM), biceps femoris (BF), and medial and lateral gastrocnemius (GM and GL). These actuators consist of servomotors (BE series, Parker Hannifan Corp., Cleveland, OH) and gearboxes (AB042, Apex Dynamics, Ronkonkoma, NY) and are connected to pulleys with steel cables providing a linear ROM of 300 mm (Table 1).

#### Sensors.

Various sensors have been implemented in the design of the UTJLS to measure forces and positions (Table 4). Musculotendon forces are measured with tension load cells (XFTC321, Measurement Specialties, Hampton, VA), which are connected at the point of each tendon's attachment (Table 2) (Fig. 2(a)). This sensor placement prevents measurement error due to friction in cable guides, and the 10 mm diameter of the tension load cells allows for the musculotendon line of action to route adjacent to bones without collision.

The rotations of the lower manipulator are mounted on spherical bearings connected to four three-axis load cells (3A120, Interface, Inc., Scottsdale, AZ) (range: 0–1000 N, accuracy: 0.3% full scale, and repeatability: 0.1% rated output) (Table 3) (Fig. 1(a)). Each three-axis load cell is mounted equidistant from the ankle's center of rotation, which provides moment arms used for moment measurement. Through the use of this custom design, the range of vertical force and x-moment measurement is configured for simultaneous, highly dynamic loading.

A six-axis load cell (Omega160, ATI Industrial Automation, Apex, NC) is attached to the hip manipulator to measure hip forces and moments (Table 3). It is located at the center of rotation of the simulated hip with the superior musculotendon actuator system located on the measurement side of the load cell, which prevents musculotendon forces from being included in the measurement (Table 4) (Fig. 1(a)).

All rotations and linear axes are equipped with absolute encoders. Linear axes, Hx and Hz, are equipped with the same model absolute encoders (EMAX 2, ELGO Electronic, Inc., Chicago, IL) (maximum speed: 4 m/s, resolution: 0.01 mm, and accuracy: 0.186 mm), and the Hy linear axis is equipped with another model absolute encoder (LMA10, Renishaw, Inc., Hoffman Estates, IL) (maximum speed: 14 m/s, resolution: 7.8 μm, and accuracy: 0.06 mm). All six MPP servomotors are equipped with an internal absolute encoder (EQI 1331, Heidenhain Corp., Schaumburg, IL).

#### Controller and Data Acquisition.

Two computers, a host computer and a real-time control computer, have been included to support the custom UTJLS software developed in LabVIEWTM version 2014 SP1 (National Instruments, Austin, TX). The host computer provides a user interface, whereas the real-time control computer operates using a LabVIEWTM real-time operating system. Control computation and data collection are performed by the real-time computer with support from a data-acquisition chassis (NI PXI-1036, National Instruments, Austin, TX) including a field-programmable gate array (NI PXI-7811 R, National Instruments, Austin, TX). This configuration provides the computing power to operate the UTJLS in real-time with a controller loop speed of 2000 Hz.

#### Electronic Hardware.

All actuators run off drivers configured for current control. Rotational motors are driven by analog brushless drives providing trapezoidal commutation through Hall state feedback (BE series, Advanced Motion Controls, Camarillo, CA), and linear motors are driven by digital drives providing sinusoidal commutation through combined encoder and Hall state feedback (DP Series, Advanced Motion Controls, Camarillo, CA). All drives receive commands from the UTJLS controller through analog signals.

Custom low voltage hardware has been included on printed circuit boards to assist in data acquisition and interfacing between equipment. Functions served by this equipment include analog signal amplification, low-pass filtering, differential to single-ended signal conversion, and digital signal amplification (Fig. 3).

#### Specimen Mounting.

A custom mounting device was developed to support correct alignment of specimens and to minimize the shape, weight, and inertia of cadaver mounting components. For both the femur and tibia, complex casting molds were developed that accommodate a large range of bone sizes without intersecting muscle paths (Fig. 2(b)). The mounting fixture has four line lasers that project two intersecting planes as guides for bone cutting and casting. During alignment, each bone was adjusted until the line lasers intersected its proximal and distal joint centers of rotation, which ensured that the mechanical axis of each bone was aligned to its respective manipulator. The effective length of each bone was matched to that of the in vivo subject by removing the proximal end of the femur and the distal end of the tibia. While maintaining proper alignment, the bone was then lowered into the mold, and polyurethane (ProtoCast 80 R, Industrial Polymers Corp., Houston, TX) was poured into the mold to secure the bone to the metal base for simulator interfacing.

### Controller Development

#### Controller Architecture and Functions.

During each loop iteration at a rate of 2000 Hz, the controller collects and stores sensor data, loads trajectory data, calculates feedback command outputs, and checks safety limits for all 29 sensors and 17 actuators. In addition, the UTJLS also provides a variety of functions to assist in cadaver testing including data review, manual subsystem control, specimen alignment, trajectory planning, and error reporting.

#### Control Strategy.

To support the accurate application of force and positions, the simulator employs a variety of control strategies that may be applied synchronously. These control strategies include feedforward force, feedforward position, force feedback, position feedback, and compensation for gravity and friction. Feedforward command voltages are determined by multiplying predicted forces by a loading constant and predicted accelerations by a mass constant, where acceleration is calculated from predicted positions using derivative estimation. Gravity compensation is configured for three axes including $θxH$, $θxA$, and Hz. The compensation for Hz is a constant voltage offset, while gravity compensation for $θxH$ and $θxA$ monitors the present rotation and adds a voltage command based on a sinusoidal fit. The friction compensators use position feedback and derivative estimation to determine the current velocity. If velocity magnitude exceeds a specified range, the controller applies a command voltage in the same direction of the measured velocity. Serving as the principal control strategy for the UTJLS, proportional–integral–derivative controllers are employed for force and position feedback, which are operated synchronously to support hybrid control.

#### Simulation Phases.

Each simulation contains multiple phases of control. The seeking phase initiates the procedure by applying tension to all tendons and ramping the specimen to the initial position of the maneuver, where it is locked in place. The simulator applies the following control sequence: ramp force controlled axes to their initial loads, ramp position controlled axes to their initial conditions, perform the maneuver, and undergo a stabilization phase when the maneuver is completed or an error has occurred. The UTJLS controller also supplies an analog signal coinciding with maneuver initiation and completion to synchronize simulator data with cadaver instrumentation.

#### User Interface.

The UTJLS user interface provides numerous features, which are separated into five categories including maneuver selection, parameter configuration, simulation, data analysis, and subcomponent operation. When a maneuver is imported or generated, it is saved on the host computer as an option presented in list form. Selection of one of these maneuvers in the interface will send the associated dataset from the host to the real-time control computer, which then may be reviewed graphically alongside feedforward commands. Parameters may be modified manually or by parameter file upload, and since every simulation outputs a copy of the current parameter file, the UTJLS can always be reverted to a previous configuration to identically recreate a test. If an error occurs during testing, the controller will immediately stabilize the simulator and display a description of the error. When a simulation is completed or an error is encountered, the program then stores the maneuver trajectories, sensor measurements, and parameter configuration to a file on the host computer.

#### Control Scheme.

The UTJLS controller's flexible architecture allows for various control schemes to be implemented. Excluding musculotendon actuators which are only configured for force control, each axis may be selected to operate with position feedback, force feedback, or hybrid feedback. Table 4 identifies the available feedback sources and the control scheme selected for squat testing.

### Squat Simulation

#### Simulator Input Data.

An athletic male (age: 20 yr, height: 1.68 m, and weight: 498 N) participated in a motion capture session where he performed five trials of two different squat techniques. The test was approved by the internal review board with informed consent. The subject was instrumented with a 37-marker set of the lower body (Northern Digital, Waterloo, ON, Canada) and electromyography electrodes on the eight muscles represented on the simulator (Delsys, Boston, MA) with one force platform (Bertec, Columbus, OH) per foot positioned shoulder width apart. The subject was instructed to squat descending for 5 s until the tops of his thighs were parallel to the ground and take 5 s returning to stance. Squats were performed with center of force directly on his heels (heel squat) and on his toes (toe squat) at the apex of the squat. A model was developed in Visaul3D (C-Motion, Inc., Germantown, MD) and allowed for three rotations and three translations at the hip, knee, and ankle joints. Lower extremity rotations, translations, moments, and ground reaction forces (GRFs) were calculated, exported, and used as inputs for the UTJLS in vitro simulations. Individual muscle forces were calculated through the calibrated EMG-informed neuromusculoskeletal modelling Toolbox, a hybrid electromyography-driven model, and input into the simulator [33].

Four lower extremity male specimens (age: 21–55 yr, side: right) were labeled M, K, U, and B. Specimen M, U, and B were partially fixed, whereas specimen K was fully fixed. While skin, adipose tissue, and fascia were removed up to the knee, the joint capsule, tendons, ligaments, and soft tissue inside of the knee were left intact. Tendons were cleaned of muscle tissue and transected 75 mm from their attachment point. Anterior incisions were made along the medial and lateral aspects of the patella to support instrumentation including a differential variable reluctance transducer (LORD Sensing, Williston, VT) and a custom pressure sensor (Teksan, Inc., Boston, MA). Posterior incisions were made superior to the medial and lateral menisci allowing insertions of the custom pressure sensor and placed anteriorly through the joint capsule superior to the meniscus. The sensor was surgically attached both anteriorly and posteriorly. Differential variable reluctance transducer was sutured onto the anteromedial bundle of the ACL. The patella incisions were sutured closed with sensors inside to mimic an intact knee capsule. Specimens were placed in the UTJLS and tendons were connected through freezer clamps (Fig. 2(a)).

Tendons were wrapped in gauze, covered in electrolyte gel, and inserted into extension hulls which were attached to tension load cells and musculotendon actuators. Tendons were frozen in liquid nitrogen to prevent damage and increase tensile strength [34]. Motion capture bone pins (Northern Digital, ON, Canada) were screwed into the femur, patella, and tibia (Fig. 2(a)).

#### Experimental Protocol.

To account for specimen geometry and fixation variability during casting, an alignment protocol was used to manually determine specimen-specific offsets for $θyH$ and $θzA$. During this protocol, the simulator applied a vertical 100 N force at 30 deg and 90 deg flexion with all other GRFs held at zero. Offsets were then iteratively adjusted until the tibial plateau forces were distributed across both the medial and lateral pressure sensor pads to replicate a 1.5:1 force distribution, respectively [35,36].

Prior to calibration testing and squat simulation, an axial preload of 500 N was applied to the specimen for pressure sensor conditioning. Pressure sensor calibration tests applied a vertical 250 N force at 60 deg flexion with all other GRFs held at zero, and the same test was applied at 30 deg flexion to measure offset of internal/external rotation (IE). Each of the four specimens underwent three heel squat tests with musculotendon force, three heel squat tests without musculotendon force, three toe squat tests with musculotendon force, and three toe squat tests without musculotendon force. Only two toe squat tests without musculotendon forces were collected from specimen K due to a labeling error. In total, data from 47 tests were collected to determine the accuracy and repeatability of the UTJLS. The magnitude of the musculotendon force profiles was scaled by 50% of in vivo estimates to prevent tendon failure during testing. Tibiofemoral contact, relative ACL strain, and relative tibiofemoral kinematics were collected for a future study identifying differences between heel and toe squat maneuvers. The VM tendon of specimen M was ruptured during testing and replaced with a threaded insert.

#### Data Conditioning.

For repeatability and accuracy analysis, the signal output from the UTJLS force sensors was low-pass filtered at 58 Hz to eliminate interference from nearby AC power, and all signals including position sensors were resampled and interpolated from 2000 Hz to provide an effective 100 Hz sampling.

#### Calculation of Anatomical Rotation.

The anatomical rotations presented in this study were determined through a vector analysis using the floating axis method described in Ref. [37]; however, the axes were not determined by bony landmarks. Rather, the anatomical axes were identified from simulator sensors assuming that the calibration protocol aligned the FE axis to the simulator's X-axis and achieved zero IE.

#### Statistical Methods.

This study assessed the short-term accuracy and precision errors of the UTJLS during the four squat maneuvers described in the experimental protocol. Standard deviations were determined for the UTJLS position and force sensors identified in Table 4 along with the three linear forces measured by the Omega160 load cell (i.e., $FxH$, $FyH$, and $FzH$). The following equations were used to calculate the standard deviation and upper limit of confidence intervals for accuracy, trial repeatability, and specimen repeatability [38]:
$SD=∑k=1m∑j=1nj∑i=1oi(xijk−y)2df(oi)$
(1)

$df=∑k=1m(nj−1)$
(2)

$σ2
(3)

where SD is standard deviation, xijk is the sensor measurement collected on specimen k during maneuver j for data point i, y is the reference value for the corresponding data point, df is the degrees-of-freedom of the test, oi is the total number of data points collected during trial j, nj is the total number of trials for specimen k, m is the total number of specimen, σ is true error, and χ2 is the chi-square distribution with probability level α/2 with df degrees-of-freedom. The reference value, y, is equal to the target trajectory for control accuracy SD, the mean average of all specimen during the same maneuver type for trial repeatability SD, and the mean average of specimen k during the same maneuver type for specimen repeatability SD. Offsets for $θyH$, $θzA$, and $θzA$ were subtracted from their respective measurements and during calculation of reference trajectories.

## Results

### Position Control Response.

The four rotation motors operating with position control feedback demonstrated excellent accuracy and trial repeatability with SDs less than 0.13 deg and 0.12 deg (Table 5). Alignment offsets for $θyH$ were 3.5 deg, 5 deg, 0.5 deg, and 5 deg, and those for $θzA$ were 2 deg, −2 deg, 2.5 deg, and −12 deg for specimens M, K, U, and B, respectively. The average result for each specimen during heel squat testing including 50% musculotendon forces is shown in Fig. 4(a).

### Force Control Response.

The seven musculotendon actuators utilized force proportional–integral–derivative control without any form of position feedback. Accuracy and trial repeatability for all musculotendon forces were less than 8 N for every axis (Table 5). These results demonstrate an excellent force response as desired for in vitro testing with no need for further force control development. The average musculotendon forces for specimen B during heel squat testing with 50% musculotendon forces are shown in Fig. 5.

### Hybrid Control Response.

Axes utilizing hybrid feedback were tuned to optimize force response. The corresponding GRFs had a maximum accuracy SD of 29 N for forces and 4.4 N·m for moments, and the corresponding SD for specimen repeatability was 12 N and 1.8 N·m (Table 5). The average result for each specimen during heel squat testing including 50% musculotendon forces is shown in Fig. 4(a).

### Dependent Variable Repeatability.

The results for sensors with no targeted output are less predictable and repeatable than those that the UTJLS monitors and controls. The SD for each axis is shown in Table 6, and the average result for each specimen during heel squat testing with 50% musculotendon forces is shown in Fig. 4(b). Alignment offsets for $θzA$ were −0.1 deg, 14.7 deg, 5.6 deg, and 7.7 deg for specimens M, K, U, and B, respectively. Included in this analysis are resultant anatomical rotations, which despite no explicit control maintained FE within an SD of 0.38 deg.

For most sensors, application of musculotendon forces minimally influenced accuracy or repeatability, but for some, the effect was substantial. For example, during heel squat testing, musculotendon forces improved the specimen repeatability RMS of $MxA$ and $FyA$ by 2.6 N·m and 6.7 N. The same change in loading increased IE specimen repeatability RMS by 0.63 deg but reduced RMS accuracy error by 6.2 deg. Anatomical knee rotations of one specimen are shown in Fig. 6.

A similar effect was measured by Tekscan instrumentation, where the introduction of musculotendon forces reduced the range of the COP travel on both sensor pads without increasing specimen repeatability. Specimen U's COP during heel squat testing is shown in Fig. 7.

## Discussion

During our preliminary work, individual actuator tests demonstrated exceptional accuracy and repeatability, but such results are not indicative of performance during physiological loading where interactions among multiple actuators increase the error. An example of such an interaction can be seen in Fig. 5, where sudden changes in flexion caused localized peaks in RMS accuracy error for musculotendon forces. Hence, system performance was assessed during simulations of four physiological maneuvers including synchronous control of up to 16 actuators.

### Control Scheme.

The control scheme of this study effectively performed knee F/E with inverse dynamics while all other knee DOFs operated in forward dynamics. This approach provided accurate and repeatable loads while also accommodating geometric variation among cadaver specimens. The desired loading was achieved in real-time despite changes in maneuver, application of musculotendon forces, and specimen.

The results also present some outcomes that are unique to this method. For example, $θyA$ was driven by force rather than position allowing for specimen-specific paths, and as a result, the moment arms between knee center and GRFs also varied throughout maneuvers and generated specimen-specific varus/valgus (VV) knee moments. Other control schemes in literature do not demonstrate this outcome [14,1719,21]. These simulators maintain constant moment arms between knee center of rotation and GRFs by fixing the tibia to the GRF load cell. The UTJLS controller can be configured to effectively match this control scheme by controlling $MyA$ and $MzA$ using $θyH$ and $θzA$. This control scheme would allow for synchronous control of $θyA$, $θzA$, $MyA$, and $MzA$, and therefore consistent application of knee VV and IE moments by GRFs for all specimen.

### Controller Response.

To date, no study has assessed simulator repeatability and accuracy during a real-time, physiological maneuver that includes musculotendon forces and multiplanar kinematics and kinetics. Time-scaled gait maneuvers of Noble et al. [18] and Maletsky and Hillberry [24], which have similar loading conditions, may serve as a reference for comparison. During simulation of physiological loads, even axes assigned a near zero or constant target experience large disturbances due to direct influence from other axes and inertial effects generated by system accelerations. Despite these disturbances, the position controlled axes and musculotendon actuators performed all tasks with minimal error (Table 5). The controller accuracy SDs of $FxA$, $FyA$, and $FzA$ with a maximum of 29 N are consistent with reported RMS errors in Refs. [18] and [24], but $MyA$ and $MzA$ with a maximum SD of 4.4 N·m were less accurate than RMS errors reported in Ref. [18] (Table 5).

Numerous factors contribute to the accuracy error of $MyA$ and $MzA$ including accuracy of reference trajectories (Fig. 4(b)), high-load capacity (Table 1) operating in a low range of operation (Fig. 4(a)), disturbances developed from other axes, disturbances from friction, limited resolution from feedback sources (Table 3), and backlash in the associated gearboxes (Table 1). These axes demonstrated superior performance during individual actuator testing and with reference trajectories tuned for a specific maneuver. The predicted trajectories for $θyA$ and $θzA$ were referenced by the hybrid controller and feedforward components of the controller, but the references did not reflect the actual paths observed during testing, which were specimen-specific and unpredictable prior to testing. Accordingly, reference trajectories tuned for each specimen and maneuver are expected to improve $MyA$ and $MzA$ performance. In future studies, improved reference trajectories may be obtained through trajectory optimization algorithms as demonstrated elsewhere [14,18,24], which have been able to improve force response by more than 85% for linear GRFs and 50% for GRF moments [14].

The UTJLS demonstrated consistent loading (Table 5), and the specimen response to that loading was repeatable (Table 6). Anatomical rotation repeatability was all less than 1.25 deg, which is reported to be sufficient for investigating passive path kinematics, a simple maneuver when compared to physiological loading [14]. While the current configuration is suitable for knee testing, improvement may be possible through trajectory optimization and addition of encoder feedback to support hybrid control of musculotendon actuators (Table 4).

### Limitations.

If the same parameters and control scheme are used during real-time UTJLS simulation of a faster maneuver, the accuracy and repeatability SDs are expected to increase beyond what was reported here. Additionally, some limitation to these results may exist due to the material properties of the partially and fully fixed specimens used in this study. For maneuvers with similar characteristics and UTJLS settings, the repeatability and accuracy of the UTJLS as presented in Tables 5 and 6 have confidence intervals that were determined with 95% confidence and have an upper limit of +42% for musculotendon actuators and +28% for all other axes and sensors.

### Future Work.

The flexible architecture of the UTJLS and its controller support testing a variety of human joints, highly dynamic maneuvers, and kinetic chains of up to two connected joints (e.g., hip and knee or knee and ankle). The primary systems of the UTJLS provide the DOFs, ROM, speed, precision, and accuracy necessary to accomplish these tasks; however, some tasks will require system adjustment that may include end effector customization, controller refinement, mounting fixture modification, and addition of the lower gantry system shown in Fig. 1(a). Recommended modifications to improve system performance include trajectory optimization and a reconfiguration of the custom GRF load cells for improved $MyA$ and $MzA$ resolution [14,18].

## Conclusion

The UTJLS can simulate physiological loads via in vitro musculoskeletal testing including real-time, synchronous application of musculotendon forces and GRFs during multiplanar kinematics. Being the first design of its kind, our simulator utilizes two separate robotic manipulators that contain a total of eight musculotendon actuators and two six-axis load cells. By adjusting the control scheme configuration, the UTJLS can match the constraints of traditional testing rigs (e.g., Oxford rig or robotic arm), recreate absolute motion to reproduce gravitational and inertial loads, and uniquely investigate joint moment contributions from GRFs as demonstrated in this study. With the necessary DOFs, ROM, and speed, the UTJLS is suitable for future testing of faster maneuvers, a variety of human joints, and a kinetic chain of two connected joints (e.g., hip and knee).

## Acknowledgment

The authors would like to thank Paul Power for his contributions to the design and development of the software and hardware for the user interface and reconfigurable controller of the UTJLS. Numerous students including Herman Cordero, Victor Contreras, Xavier Villarreal, and Javier Ornelas provided invaluable support that made this project possible.

## Funding Data

• National Science Foundation (Grant No. BES 0966398).

• The University of Texas STARS Funding.

• ADVANCED Motion Controls University Outreach Program.

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