Resultant Joint Moments Research Articles

Mechanics of the foot and ankle joints during running using a multi-segment foot model compared with a single-segment model.

The primary purpose of this study was to compare the ankle joint mechanics, during the stance phase of running, computed with a multi-segment foot model (MULTI; three segments) with a traditional single segment foot model (SINGLE). Traditional ankle joint models define all bones between the ankle and metatarsophalangeal joints as a single rigid segment (SINGLE). However, this contrasts with the more complex structure and mobility of the human foot, recent studies of walking using more multiple-segment models of the human foot have highlighted the errors arising in ankle kinematics and kinetics by using an oversimplified model of the foot. This study sought to compare whether ankle joint kinematics and kinetics during running are similar when using a single segment foot model (SINGLE) and a multi-segment foot model (MULTI). Seven participants ran at 3.1 m/s while the positions of markers on the shank and foot were tracked and ground reaction forces were measured. Ankle joint kinematics, resultant joint moments, joint work, and instantaneous joint power were determined using both the SINGLE and MULTI models. Differences between the two models across the entire stance phase were tested using statistical parametric mapping. During the stance phase, MULTI produced ankle joint angles that were typically closer to neutral and angular velocities that were reduced compared with SINGLE. Instantaneous joint power (p<0.001) and joint work (p<0.001) during late stance were also reduced in MULTI compared with SINGLE demonstrating the importance of foot model topology in analyses of the ankle joint during running. This study has highlighted that considering the foot as a rigid segment from ankle to MTP joint produces poor estimates of the ankle joint kinematics and kinetics, which has important implications for understanding the role of the ankle joint in running.

How the acceleration phase influences energy flow and the resulting joint moments of the throwing shoulder in the deceleration phase of the javelin throw.

The throwing motion in the javelin throw applies high loads to the musculoskeletal system of the shoulder, both in the acceleration and deceleration phases. While the loads occurring during the acceleration phase and their relationship to kinematics and energy flow have been relatively well investigated, there is a lack of studies focusing the deceleration phase. Therefore, the aim of this study is to investigate how the throwing arm is brought to rest, which resultant joint torques are placed on the shoulder and how they are influenced by the kinematics of the acceleration phase. The throwing movement of 10 javelin throwers were recorded using a 12-infrared camera system recording at 300 Hz and 16 markers placed on the body. Joint kinematics, kinetics and energy flow were calculated between the touchdown of the rear leg and the timepoint of maximum internal rotation after release +0.1 s. Elastic net regularization regression was used to predict the joint loads in the deceleration phase using the kinematics and energy flow of the acceleration phase. The results show that a significant amount of energy is transferred back to the proximal segments, while a smaller amount of energy is absorbed. Furthermore, relationships between the kinematics and the energy flow in the acceleration phase and the loads placed on the shoulder joint in the deceleration phase, based on the elastic net regularized regression, could be established. The results indicate that the loads of the deceleration phase placed on the shoulder can be influenced by the kinematics of the acceleration phase. For example, an additional upper body forward tilt can help to increase the braking distance of the arm and thus contribute to a reduced joint load. Furthermore, the energy flow of the acceleration phase can be linked to joint stress. However, as previously demonstrated the generation of mechanical energy at the shoulder seems to have a negative effect on shoulder loading while the transfer can help optimize the stress. The results therefore show initial potential for optimizing movement, to reduce strain and improve injury prevention in the deceleration phase.

Biomechanical effects of fatigue on lower-body extremities during a maximum effort kettlebell swing protocol

ABSTRACT Kettlebell training provides multiple health benefits, including the generation of power. The primary purpose of this study was to examine the kinematics and kinetics of lower-body joints during a repeated, maximum effort kettlebell swing protocol. Sixteen resistance and kettlebell swing experienced males performed 10 rounds of a kettlebell swing routine (where one round equates to 30s of swings followed by 30s of rest). Kinematic (i.e., swing duration and angular velocities) and kinetic (i.e., normalised sagittal plane ground reaction force, resultant joint moment [RJM] and power) variables were extracted for the early portion and late portion of the round. Average swing duration and the magnitude of normalised ground reaction forces (GRF) increased within rounds, while hip joint power decreased. Changes in swing duration were minimal, but consistent due to an increase in overall fatigue. An increase in the magnitude of GRF was observed at the end of rounds, which is a potential concern for injury. Hip joint power decreased primarily due to a slower angular velocity. This protocol may be an effective routine for those who are resistance trained with kettlebell swing experience, and who want to optimise power in their exercise program.

Prediction of ground reaction forces and moments during walking in children with cerebral palsy.

Gait analysis is increasingly used to support clinical decision-making regarding diagnosis and treatment planning for movement disorders. As a key part of gait analysis, inverse dynamics can be applied to estimate internal loading conditions during movement, which is essential for understanding pathological gait patterns. The inverse dynamics calculation uses external kinetic information, normally collected using force plates. However, collection of external ground reaction forces (GRFs) and moments (GRMs) can be challenging, especially in subjects with movement disorders. In recent years, a musculoskeletal modeling-based approach has been developed to predict external kinetics from kinematic data, but its performance has not yet been evaluated for altered locomotor patterns such as toe-walking. Therefore, the goal of this study was to investigate how well this prediction method performs for gait in children with cerebral palsy. The method was applied to 25 subjects with various forms of hemiplegic spastic locomotor patterns. Predicted GRFs and GRMs, in addition to associated joint kinetics derived using inverse dynamics, were statistically compared against those based on force plate measurements. The results showed that the performance of the predictive method was similar for the affected and unaffected limbs, with Pearson correlation coefficients between predicted and measured GRFs of 0.71-0.96, similar to those previously reported for healthy adults, despite the motor pathology and the inclusion of toes-walkers within our cohort. However, errors were amplified when calculating the resulting joint moments to an extent that could influence clinical interpretation. To conclude, the musculoskeletal modeling-based approach for estimating external kinetics is promising for pathological gait, offering the possibility of estimating GRFs and GRMs without the need for force plate data. However, further development is needed before implementation within clinical settings becomes possible.

Positive influence of neuromuscular training on knee injury risk factors during cutting and landing tasks in elite youth female handball players

Anterior cruciate ligament (ACL) ruptures are frequent in the age group of 15–19 years, particularly for female athletes. Although injury-prevention programs effectively reduce severe knee injuries, little is known about the underlying mechanisms and changes of biomechanical risk factors. Thus, this study analyzes the effects of a neuromuscular injury-prevention program on biomechanical parameters associated with ACL injuries in elite youth female handball players. In a nonrandomized, controlled intervention study, 19 players allocated to control (n = 12) and intervention (n = 7) group were investigated for single- and double-leg landings as well as unanticipated side-cutting maneuvers before and after a 12-week study period. The lower-extremity motion of the athletes was captured using a three-dimensional motion capture system consisting of 12 infrared cameras. A lower-body marker set of 40 markers together with a rigid body model, including a forefoot, rearfoot, shank, thigh, and pelvis segment in combination with two force plates was used to determine knee joint angles, resultant external joint moments, and vertical ground reaction forces. The two groups did not differ significantly during pretesting. Only the intervention group showed significant improvements in the initial knee abduction angle during single leg landing (p = 0.038: d = 0.518), knee flexion moment during double-leg landings (p = 0.011; d = −1.086), knee abduction moment during single (p = 0.036; d = 0.585) and double-leg landing (p = 0.006; d = 0.944) and side-cutting (p = 0.015;d = 0.561) as well as vertical ground reaction force during double-leg landing (p = 0.004; d = 1.482). Control group demonstrated no significant changes in kinematics and kinetics. However, at postintervention both groups were not significantly different in any of the biomechanical outcomes except for the normalized knee flexion moment of the dominant leg during single-leg landing. This study provides first indications that the implementation of a training intervention with specific neuromuscular exercises has positive impacts on biomechanical risk factors associated with ACL injury risk and, therefore, may help prevent severe knee injuries in elite youth female handball players.

Relationships between Racket Arm Joint Moments and Racket Head Speed during the Badminton Jump Smash Performed by Elite Male Malaysian Players

Three-dimensional position data of nineteen elite male Malaysian badminton players performing a series of maximal jump smashes were collected using a motion capture system. A ‘resultant moments’ inverse dynamics analysis was performed on the racket arm joints (shoulder, elbow and wrist). Relationships between racket head speed and peak joint moments were quantified using correlational analyses, inclusive of a Benjamini–Hochberg correction for multiple-hypothesis testing. The racket head centre speed at racket–shuttlecock contact was, on average, 61.2 m/s with a peak of 68.5 m/s which equated to average shuttlecock speeds of 95.2 m/s with a peak of 105.0 m/s. The correlational analysis revealed that a larger shoulder internal rotation moment (r = 0.737), backwards shoulder plane of elevation moment (r = 0.614) and wrist extension moment (r = −0.564) were associated with greater racket head centre speed at racket–shuttlecock contact. Coaches should consider strengthening the musculature associated with shoulder internal rotation, plane of elevation and wrist extension. This work provides a unique analysis of the joint moments of the racket arm during the badminton jump smash performed by an elite population and highlights significant relationships between racket head speed and peak resultant joint moments.

Proactive Modulation in the Spatiotemporal Structure of Muscle Synergies Minimizes Reactive Responses in Perturbed Landings.

Stability training in the presence of perturbations is an effective means of increasing muscle strength, improving reactive balance performance, and reducing fall risk. We investigated the effects of perturbations induced by an unstable surface during single-leg landings on the mechanical loading and modular organization of the leg muscles. We hypothesized a modulation of neuromotor control when landing on the unstable surface, resulting in an increase of leg muscle loading. Fourteen healthy adults performed 50 single-leg landings from a 30 cm height onto two ground configurations: stable solid ground (SG) and unstable foam pads (UG). Ground reaction force, joint kinematics, and electromyographic activity of 13 muscles of the landing leg were measured. Resultant joint moments were calculated using inverse dynamics and muscle synergies with their time-dependent (motor primitives) and time-independent (motor modules) components were extracted via non-negative matrix factorization. Three synergies related to the touchdown, weight acceptance, and stabilization phase of landing were found for both SG and UG. When compared with SG, the motor primitive of the touchdown synergy was wider in UG (p < 0.001). Furthermore, in UG the contribution of gluteus medius increased (p = 0.015) and of gastrocnemius lateralis decreased (p < 0.001) in the touchdown synergy. Weight acceptance and stabilization did not show any statistically significant differences between the two landing conditions. The maximum ankle and hip joint moment as well as the rate of ankle, knee, and hip joint moment development were significantly lower (p < 0.05) in the UG condition. The spatiotemporal modifications of the touchdown synergy in the UG condition highlight proactive adjustments in the neuromotor control of landings, which preserve reactive adjustments during the weight acceptance and stabilization synergies. Furthermore, the performed proactive control in combination with the viscoelastic properties of the soft surface resulted in a reduction of the mechanical loading in the lower leg muscles. We conclude that the use of unstable surfaces does not necessarily challenge reactive motor control nor increase muscle loading per se. Thus, the characteristics of the unstable surface and the dynamics of the target task must be considered when designing perturbation-based interventions.

Tibiofemoral joint contact forces during gait differ with radiographic knee oa progression over 3 years

Purpose: Forces on joint tissues during activities of daily living such as walking have been implicated in the progression of knee osteoarthritis (OA), however the relationship between force characteristics with osteoarthritis processes is complex. It remains unclear why knee OA progresses more quickly for some individuals, and if person-specific mechanics are an important factor. Most past investigations have reported net resultant joint moments calculated through an inverse dynamics procedure that provide a net summary of joint kinetics.

Neuromechanics of Dynamic Balance Tasks in the Presence of Perturbations.

Understanding the neuromechanical responses to perturbations in humans may help to explain the reported improvements in stability performance and muscle strength after perturbation-based training. In this study, we investigated the effects of perturbations, induced by unstable surfaces, on the mechanical loading and the modular organization of motor control in the lower limb muscles during lunging forward and backward. Fifteen healthy adults performed 50 forward and 50 backward lunges on stable and unstable ground. Ground reaction forces, joint kinematics, and the electromyogram (EMG) of 13 lower limb muscles were recorded. We calculated the resultant joint moments and extracted muscle synergies from the stepping limb. We found sparse alterations in the resultant joint moments and EMG activity, indicating a little if any effect of perturbations on muscle mechanical loading. The time-dependent structure of the muscle synergy responsible for the stabilization of the body was modified in the perturbed lunges by a shift in the center of activity (later in the forward and earlier in the backward lunge) and a widening (in the backward lunge). Moreover, in the perturbed backward lunge, the synergy related to the body weight acceptance was not present. The found modulation of the modular organization of motor control in the unstable condition and related minor alteration in joint kinetics indicates increased control robustness that allowed the participants to maintain functionality in postural challenging settings. Triggering specific modulations in motor control to regulate robustness in the presence of perturbations may be associated with the reported benefits of perturbation-based training.

Assessing potential trade-offs between the lower back and shoulders: influence of lift training intervention on joint demands

Background. Many of the approaches available for modifying manual materials handling (MMH) exertion emphasize lower back protection but often do not consider how interventions affect other body regions. This study focused on the influence of lift training on resultant joint moments and muscular demand trade-offs between the lower back and shoulders during MMH tasks. Methods. Three recommended lifting techniques (straddle lift, pivot technique and tripod lift) were compared to a priori (untrained) self-selected lifting techniques. Results. Mean and cumulative resultant moments indicated that using the lifting techniques evaluated in this investigation protected the shoulders more than the lower back. Mean and peak shoulder muscle activity also decreased following training (p < 0.05). Although there were no peak and mean changes to lower back muscle activity (p>0.05), there was a significant decrease in cumulative lower back muscle activity (p < 0.05). Reported perceived exertion values decreased following training across the lifting techniques for all evaluated body regions (p < 0.05). Conclusion. Overall, the recommended MMH techniques protected both the lower back and the shoulders, and no exposure trade-offs between them were identified.

Leverage mechanical alterations during walking at self-selected speed in patients with Parkinson’s disease

Individuals with Parkinson’s disease (PD) show poor walking performance compared to healthy adults. Leverage changes may provide insight into this walking abnormality, since they have important effects on both biomechanical and physiological variables. Hence, we investigated the differences in internal and external moment arms at the knee and ankle joints, as well as the effective mechanical advantage during walking at self-selected speed. Furthermore, the effects on walking of a simultaneous cognitive task were analysed.Kinetic (resultant ground reaction force and joint moments), kinematic (movement speed) and mechanical leverage (internal and external moment arms) parameters of 10 mild-to-moderate PD patients and 10 age-matched controls were measured in single and dual task condition. Finally, effective mechanical advantage was calculated as the ratio between internal and external moment arm for each joint.PD patients had a slower walking and showed larger and lower values of knee and ankle joint moments, respectively. No difference in force among groups was recorded. External moment arms were larger (in both joints) for PD, whereas slight changes were observed for internal moment arms. Consequently, effective mechanical advantage values seemed to be lower for PD. Surprisingly, leverage difference among groups was reduced during the dual task condition, resulting in a “more effective” walking strategy for PD.These findings suggest that during single task PD patients have several leverage disadvantages, which could affect the joint assessment. On the contrary, during dual task they reduced these mechanical negative effects by positively obtaining normal values of effective mechanical advantage.

Effects of kettlebell mass on lower-body joint kinetics during a kettlebell swing exercise

ABSTRACT Functional training aims to provide specific adaptations due to exercise training and utilises a variety of equipment, including kettlebells. Due to the training principle of overload, a greater resistance must be applied to yield increased strength results. This study examined the effects of kettlebell mass on lower body joint kinetics in young recreationally trained adults. Thirty recreationally active, college-aged adults were recruited for this study. Participants performed hip-hinge style swings with kettlebells equivalent to 10%, 15% and 20% of their respective body mass. 3-D marker coordinate data were captured via infrared camera system and ground reaction force data were measured with two force plates. The resultant joint moments of the lower body were calculated using the inverse dynamics procedure. As mass increased, there was an increase in joint moment at the L4/5, hip and ankle joint, primarily due to an increase in ground reaction force. Increasing kettlebell mass can potentially cause greater strength gains in the hip and trunk musculature due to increase in lower body moments, while avoiding excessive moments about the knee.

Reaction Force Generation and Mechanical Demand Imposed on the Shoulder When Initiating Manual Wheelchair Propulsion and at Self-Selected Fast Speeds.

Manual wheelchair (WC) users with spinal cord injury (SCI) experience shoulder pain and fatigue associated with their increased reliance on the upper extremity during activities of daily living (Bayley et al. 1987, "The Weight-Bearing Shoulder. The Impingement Syndrome in Paraplegics," J. Bone Jt. Surg. Am., 69(5), pp. 676-678). We hypothesized that the mechanical demand imposed on the shoulder, represented as resultant shoulder net joint moment (NJM) impulse, would be greater when initiating manual WC propulsion from a stationary position without momentum than when manually propelling at speed on a level sidewalk. Thirty manual WC users with paraplegia participated. Each individual initiated manual WC propulsion from a stationary position and propelled on a level sidewalk at their self-selected fast speed. Upper extremity kinematics and pushrim reaction forces (RFs) were measured and upper extremity joint kinetics were calculated and compared (α = 0.05) between cycle 1, initiated without momentum, and cycle 3 with momentum. Results indicate that multiple factors contributing to the mechanical demand imposed on the shoulder were significantly greater when manual WC propulsion was initiated without momentum than with momentum. Significant differences in resultant shoulder NJM impulse, push duration, orientation of RF relative to forearm, and resultant average shoulder NJMs during push were observed between momentum conditions. No significant differences in average resultant RF during push were found. These results indicate that mechanical loading of the shoulder during manual WC propulsion differs between momentum conditions; these differences in resultant shoulder NJM impulse during push need to be considered when assessing shoulder load exposure in stop-and-start activities.

Effects of body weight support and pedal stance width on joint loading during pinnacle trainer exercise

BackgroundA pinnacle trainer is a stair climber that has a biplane exercise trajectory and an adjustable pedal stance width (PSW). A pinnacle trainer integrated with a body weight support (BWS) system can help overweight individuals or individuals with poor balance exercise safely by reducing excessive or improper joint loads, preventing training-related injuries. However, few studies have investigated the biomechanical features of the lower extremities during pinnacle trainer exercise with and without partial BWS for various PSWs. Research questionWe aimed to investigate the effects of partial BWS and PSW on the joint loading of the lower extremities during stepping on a pinnacle trainer. MethodsSeventeen healthy adults exercised on the pinnacle trainer with or without BWS using various PSWs. The joint resultant forces and joint moments of the lower extremities were calculated according to the kinematic and kinetic data measured via a motion capture system and force transducers on the pedals, respectively. ResultsThe joint resultant forces and joint moments of the lower extremities significantly decreased with increasing percentage of BWS. The internal knee adduction moment and internal hip abduction moment significantly increased with increasing PSW. For every kilogram of BWS, the joint loading of the lower extremities decreased by approximately 1% of the joint resultant forces of body weight during exercise with the pinnacle trainer. SignificanceExercise on the pinnacle trainer with partial BWS significantly reduced joint loading. Exercise with a wider pedal stance may be helpful for knee osteoarthritis rehabilitation as it produces greater internal hip abduction and internal knee adduction moments.

Dynamics of submaximal effort soccer instep kicking

ABSTRACTDuring a soccer match, players are often required to control the ball velocity of a kick. However, little information is available for the fundamental qualities associated with kicking at various effort levels. We aimed to illustrate segmental dynamics of the kicking leg during soccer instep kicking at submaximal efforts. The instep kicking motion of eight experienced university soccer players (height: 172.4 ± 4.6 cm, mass: 63.3 ± 5.2 kg) at 50, 75 and 100% effort levels were recorded by a motion capture system (500 Hz), while resultant ball velocities were monitored using a pair of photocells. Between the three effort levels, kinetic adjustments were clearly identified in both proximal and distal segments with significantly different (large effect sizes) angular impulses due to resultant joint and interaction moments. Also, players tended to hit an off-centre point on the ball using a more medial contact point on the foot and with the foot in a less upright position in lower effort levels. These results suggested that players control their leg swing in a context of a proximal to distal segmental sequential system and add some fine-tuning of the resultant ball velocity by changing the manner of ball impact.

Upper-limb biomechanical analysis of wheelchair transfer techniques in two toilet configurations

BackgroundUsing proper technique is important for minimizing upper limb kinetics during wheelchair transfers. The objective of the study was to 1) evaluate the transfer techniques used during toilet transfers and 2) determine the impact of technique on upper limb joint loading for two different toilet configurations. MethodsTwenty-six manual wheelchair users (23 men and 3 women) performed transfers in a side and front wheelchair-toilet orientation while their habitual transfer techniques were evaluated using the Transfer Assessment Instrument. A motion analysis system and force sensors were used to record biomechanical data during the transfers. FindingsMore than 20% of the participants failed to complete five transfer skills in the side setup compared to three skills in the front setup. Higher quality skills overall were associated with lower peak forces and moments in both toilet configurations (−0.68 < r < −0.40, p < 0.05). In the side setup, participants who properly placed their hands in a stable position and used proper leading handgrips had lower shoulder resultant joint forces and moments than participants who did not perform these skills correctly (p ≤ 0.04). In the front setup, positioning the wheelchair within three inches of the transfer target was associated with reduced peak trailing forces and moments across all three upper limb joints (p = 0.02). InterpretationTransfer skills training, making toilet seats level with the wheelchair seat, positioning the wheelchair closer to the toilet and mounting grab bars in a more ideal location for persons who do sitting pivot transfers may facilitate better quality toilet transfers.

Optimization-based motor control of a Paralympic wheelchair athlete

The following research approximated how the central nervous system of Paralympic wheelchair athletes resolve kinematic redundancies during upper-limb movements. A multibody biomechanical model of a tetraplegic Paralympic athlete was developed using subject-specific body segment parameters. The angular joint kinematics throughout a specified Paralympic sport movement (i.e., wheelchair curling) were experimentally measured using inertial measurement units. The motor control system of the Paralympian was mathematically modelled and simulated using forward dynamics optimization. The predicted kinematics from different optimization objective functions (i.e., minimizing resultant joint moments, mechanical joint power, and angular joint velocities and accelerations) were compared with those experimentally measured throughout the wheelchair curling movement. Of the optimization objective functions under consideration, minimizing angular joint accelerations produced the most accurate predictions of the kinematic trajectories (i.e., characterized with the lowest overall root mean square deviations) and the shortest optimization computation time. The implications of these control findings are discussed with regards to optimal wheelchair design through predictive dynamic simulations.

Joint kinetic determinants of starting block performance in athletic sprinting

ABSTRACT The aim of this study was to explore the relationships between lower limb joint kinetics, external force production and starting block performance (normalised average horizontal power, NAHP). Seventeen male sprinters (100 m PB, 10.67 ± 0.32 s) performed maximal block starts from instrumented starting blocks (1000 Hz) whilst 3D kinematics (250 Hz) were also recorded during the block phase. Ankle, knee and hip resultant joint moment and power were calculated at the rear and front leg using inverse dynamics. Average horizontal force applied to the front (r = 0.46) and rear (r = 0.44) block explained 86% of the variance in NAHP. At the joint level, many “very likely” to “almost certain” relationships (r = 0.57 to 0.83) were found between joint kinetic data and the magnitude of horizontal force applied to each block although stepwise multiple regression revealed that 55% of the variance in NAHP was accounted for by rear ankle moment, front hip moment and front knee power. The current study provides novel insight into starting block performance and the relationships between lower limb joint kinetic and external kinetic data that can help inform physical and technical training practices for this skill.

Inverse Dynamics Modeling of Paralympic Wheelchair Curling

Paralympic wheelchair curling is an adapted version of Olympic curling played by individuals with spinal cord injuries, cerebral palsy, multiple sclerosis, and lower extremity amputations. To the best of the authors' knowledge, there has been no experimental or computational research published regarding the biomechanics of wheelchair curling. Accordingly, the objective of the presentresearch was to quantify the angular joint kinematics and dynamics of a Paralympic wheelchair curler throughout the delivery. The angular joint kinematics of the upper extremity were experimentally measured using an inertial measurement unit system; the translational kinematics of the curling stone were additionally evaluated with optical motion capture. The experimental kinematics were mathematically optimized to satisfy the kinematic constraints of a subject-specific multibody biomechanical model. The optimized kinematics were subsequently used to compute the resultant joint moments via inverse dynamics analysis. The main biomechanical demands throughout the delivery (ie, in terms of both kinematic and dynamic variables) were about the hip and shoulder joints, followed sequentially by the elbow and wrist. The implications of these findings are discussed in relation to wheelchair curling delivery technique, musculoskeletal modeling, and forward dynamic simulations.

A bistable rolling joint for multistable structures

In this paper, a concept of using rolling joints for a multistable structure, which deforms elastically into a variety of cylindrical shapes, is presented. A bistable joint is obtained by modifying the geometry of a rolling hinge. The proposed concept can hold the stable state without any continued actuation. Then detailed mathematical derivations are carried out to obtain the wire tensions and joint resultant moment during the motion, which are used to compute the external action that should be applied to move the joint. The effects of some geometric parameters on the mechanical behavior are also investigated. The results show that higher values of the wire tension and joint resultant moments can be obtained by increasing the side included angle φ or the radius of wire wrapped circles R. Moreover, the pretension of wires in the stable configuration also increases the wire tension and the joint resultant moment.