Abstract
This study presents and applies 3D spherical angular analysis in relation with 2D polar coordinates to assess anatomic pelvic movement on modified gait, namely stiff knee (SKG) gait and slow running (SR) comparing with normal gait (NG). Subject specific analysis was performed of an adult healthy male based on inverse kinematics from in vivo and noninvasive capture at human movement lab of reflective markers position from pelvis anatomical selected points with Qualisys camera system during a complete stride of NG, SKG and SR. Radial distance (R), pitch (psi) and azimuth (lambda) angular phases were computed from pelvic angle-angle diagrams (theta(T), theta(C), theta(S)) at transverse (T), coronal (C) and sagittal (S) planes, and angular phase (phi) and planar radial distance (r) polar coordinates computed from pelvic angle-angle diagrams projections at cartesian planes (theta(T), theta(C)), (theta(T), theta(S)), (theta(C), theta(S)). Average radial distances and phase standard deviation were assessed on spherical and polar coordinates.

Abstract
This study assesses in vivo and noninvasive human lower limb dynamic stiffness at different muscle stretch-shortening cycle (SSC) on maximum vertical jump (MVJ) with long, short and without countermovement. A small sample of n=6 healthy young adult male students of sports and physical education degree without past injuries, specific training or sports record were assessed after informed consent according to the world medical association declaration of Helsinki. Subjects were weighted (76.7 +/- 9.3) kg and their height measured (178.9 +/- 6.3) cm performing each three trials of MVJ namely squat jump (SJ), countermovement jump (CMJ) and drop jump (DJ) from a step with 40 cm height. Ground reaction forces (GRF) were acquired during impulse phase with AMTI force plate BP2416-4000 CE and Mini Amp MAS-6 amplifier at 1000 Hz. Vertical acceleration (a(z)) of whole body center of gravity (BCG) obtained from resultant vertical ground reaction force (RFz) was time integrated twice for calculation of vertical displacement (Delta z) of BCG and dynamic stiffness obtained from slopes at different segmented subphases of RFz mass normalized RFz/m vs Delta z plot during impulse phase. Results of vertical dynamic stiffness during impulse phase point for inter-subject similarities at each type of MVJ and statistical significative differences (p<0.05) between SJ, CMJ and DJ with impact on MVJ optimization.

Abstract
This study presents and applies noninvasive subject specific validation of human whole-body (WB) center of mass (COM) kinematic from 3D anthropometric multibody model using dynamic data from ground reaction forces during impulse phase at standard maximum vertical jump (MVJ) with long countermovement (CM) on countermovement jump (CMJ) and short CM on drop jump (DJ) for comparison with MVJ without CM on squat jump (SJ), assessing lower limb CM contribution and muscle stretch-shortening cycle (SSC) at WB COM vertical impulse. A small group of n = 6 sports and physical education degree students with (21.5 ± 1.4) years old, without previous injuries, specific sport abilities or train were weighed (76.7 ± 9.3) kg and their height measured (1.79 ± 0.06) m. Adhesive reflective marks were attached at main upper and lower limb joints. Each subject performed a total of 3 trial at each MVJ, CMJ, DJ and SJ. During trial tests kinematics of anatomical points were registered with two JVC GR-VL9800 digital video cameras at 100 Hz and ground reaction forces with AMTI platform model BP2416-4000 CE operating at 1000 Hz. WB COM kinematics was determined using calibrated SIMI motion tracking of joint reflective marks and Dempster model selecting vertical WB COM displacement ?zk according to higher amplitude and research interest on MVJ WB COM movement for CM and SSC assessment. Dynamic of WB COM vertical displacement ?zd was determined from double time integration of COM vertical acceleration. Comparison of kinematic ?zk and dynamic ?zd was statistically tested on average and variance at each MVJ type, ?zk with ?zd and on root mean square-error (RMSE) during impulse phase. Results present similar variability of ?zk and ?zd at each MVJ p &gt; 0.05, with mean values discriminating CMJ different means p &lt; 0.05 from DJ and SJ with equal means p &gt; 0.05, pointing dynamic data as suitable for validation of WB COM movement from 3D anthropometric image as well as for detection of different RMSE at each type of MVJ, its influence on assessment of CM and SSC and improve accuracy on kinematic, dynamic measurements and models. © Springer Nature Switzerland AG 2019.

Abstract
This study presents innovative analysis at the time, frequency and phase domain for lower limb joint angular coordination assessment at sagittal plane on human vertical countermovement (CM), comparing long CM on countermovement jump (CMJ) and short CM on drop jump (DJ) from 40 cm step with squat jump (SJ) in the absence of CM. Lower limb CM and muscle stretch-shortening cycle has been pointed as playing a key role on human gait efficiency as well as on run and jump performance with an open issue on objective and quantitative measures for lower limb joint angle coordination assessment at different CM in comparison with no CM condition. Case study is considered from subject specific with 20 years old, 84 kg of body mass and 1.84 m height, selected according to best performance criteria of maximum vertical jump height during CMJ, DJ and SJ from a small sample of n = 6 sports and physical education degree students with (21.5 ± 1.4) years old, (76.7 ± 9.3) kg mass and (1.79 ± 0.06) m height, with no previous injuries, specific sport abilities or training. Calibrated image system with two digital video cameras JVC GR-VL9800 operating at 100 Hz and direct linear transformation (DLT-11) was used along with Simi Motion System and Dempster adapted model with 14 segments to track 3D coordinates of joint marks and obtain joint angles, angular velocities and accelerations at sagittal plane by inverse kinematics. Entire signal analysis was implemented on complementary time, frequency and phase domains for lower limb joint angle coordination assessment at sagittal plane on human vertical jump for comparison of long, short and without CM condition. Comprehensive signal analysis allowed detection of distinct coordination at CMJ from DJ and SJ as well from untrained tested subjects to those reported on trained subjects namely with lower coordination at untrained subjects associated to inaptitude to potentiate short CM and thus presenting lower DJ performance than trained subjects. © Springer Nature Switzerland AG 2019.

Abstract
This study presents subject specific analysis at complementary time, frequency and phase plane domains of entire lower limb joint angular kinematic series during normal and modified gait. Healthy adult subject case study was assessed at human movement lab during normal gait, stiff knee gait and slow running. In vivo and non-invasive assessment was performed with eight camera Qualisys system at 100 Hz acquisition of cartesian coordinates of skin reflective markers at lower limb anatomical selected point. Inverse kinematics was performed using AnyGait v.0.92 and TLEM model to match the size and joint morphology of the stick-figure. Entire series of subject specific hip, knee and ankle joint angular displacements (?), angular velocities (?) and angular accelerations (a) at the sagittal plane were assessed at the time, frequency and phase plane domains providing useful information for development of subject specific rehabilitation equipment towards gait restoring. The main novelty and contribution of this study when compared with available literature consists on complementary approach of continuous entire signal analysis, time, frequency and phase analysis which can contribute for prescription of requisites for design of rehabilitation equipment towards normal gait of subjects with stiff knee gait and slow running. © 2019, CISM International Centre for Mechanical Sciences.

Abstract