The purpose of this study was to compare the shoulder resultant joint moment (RJM) during a shoulder internal rotator exercise using elastic resistance employing four different movement strategies and two different starting elastic strains. Methods: Ten subjects aged 27.4 ± 2.6 yr (5 female and 5 male) with no previous shoulder pathology performed four sets of six repetitions of shoulder rotation though 180° using elastic resistance (Thera-Band® elastic band, blue) during two acceleration (medium and low) and two cadence (2s:2s, <1s:1s) strategies at 0% elastic starting strain. The acceleration movement strategies were also performed with starting strain of 30%. A mathematical model using Newtonian mechanics was used to compute the RJM. Elastic band recoil force was measured with a force transducer. Forearm acceleration was determined by a miniature uniaxial accelerometer secured at the wrist. Electrogoniometer data were collected to determine the range of motion (ROM) as well as the angle between the forearm and band which was used to determine elastic moment arm. Paired t-tests were used to identify joint angle specific RJM differences between conditions. Results: Angle specific comparisons revealed that RJM in the moderate acceleration movement strategy was significantly different from RJM in the low acceleration movement strategy through 150° (83%) of range of motion (p<0.05). Shoulder RJM was up to 111% higher in the moderate acceleration strategy (P < 0.01). Angle specific comparisons revealed RJM in the <1:1 cadence strategy was significantly different from RJM in the 2:2 cadence through 108° (60%) of the range of motion (p<0.05). RJM was up to 47% higher in the <1:1 cadence (p<0.01). RJM in the low acceleration strategy was significantly greater with 30% elastic start strain relative to 0% elastic start strain through 180º of angular excursion (p<0.001). The pattern and magnitude of neuromuscular loading was significantly different in higher acceleration movement strategies (moderate acceleration and fast cadence). Conclusions: These findings indicate that differential limb acceleration as a result of movement strategy significantly affects shoulder load during elastic resistance exercise. The pattern and magnitude of load was different in each movement strategy and could result in differential neuromuscular adaptation through training. Clinicians and exercise professionals should consider movement strategy/acceleration as an important factor when prescribing elastic resistance exercise for safety and efficacy. / October 2006

Drilling is a standard process for producing holes in metal materials. With an increased hole depth the demands increase on both machine and tool. Deep hole drilling is a complex process which ischaracterized by a high metal removal rate and hole accuracy. A hole deeper than ten times the diameter can be considered a deep hole which requires a specialized drilling technique. During adeep hole drilling process, the forces generated on the deep hole drill give a rise to a resultant radial force. The resultant radial force pushes the drill in a radial direction during a drilling operation. The radial force direction is of crucial importance in regard of tool guidance, stability and hole size accuracy. This force affects tool performance, reduces tool life and has an impact on the bore surface. Due to the complex nature of deep hole drilling, Sandvik Coromant wishes to get a better understanding of how their current deep hole drilling tools are balanced. The purpose of this study is to conduct a survey of a number of drills of Sandvik Coromant deep hole drill assortment. The main aim of this study is to calculate and measure the resultant radial force generated during a deep hole drilling operation. The forces are calculated with the aid of a calculation program and test-runs on a number of drills. This report presents the calculated magnitude and direction of the resultant radial force duringentrance, full intersection and at the exit of the workpiece. In addition to the measured values of theresultant radial force during entry and full intersection. Four different drill geometries are evaluated which of two are competitor drills. A deep hole drill geometry is re-modified in aspect to drill stability based on the outcome of the measured and calculated results. The results acquired from the performed calculation and measurements of the resultant showed that the resultant radial force acts in an angular direction that was outside the range between the support pads. This true for three of the four evaluated drill geometries. There were minor differences between the measured and calculated forces which enforce the reliability of the used calculation program. The modified drill geometry of a deep hole drill gave an indication of which geometry variables have impact on the resultant radial force magnitude and angular direction. The data presented in this report can be a base for future development of a deep hole drill toolgeometry in regard to the resultant radial force. Variables affecting the calculated results and theresultant radial force are presented and discussed. The study is concluded with suggestions of futurework based on the acquired data.

The purpose of this study was to compare the shoulder resultant joint moment (RJM) during a shoulder internal rotator exercise using elastic resistance employing four different movement strategies and two different starting elastic strains. Methods: Ten subjects aged 27.4 ± 2.6 yr (5 female and 5 male) with no previous shoulder pathology performed four sets of six repetitions of shoulder rotation though 180° using elastic resistance (Thera-Band® elastic band, blue) during two acceleration (medium and low) and two cadence (2s:2s, <1s:1s) strategies at 0% elastic starting strain. The acceleration movement strategies were also performed with starting strain of 30%. A mathematical model using Newtonian mechanics was used to compute the RJM. Elastic band recoil force was measured with a force transducer. Forearm acceleration was determined by a miniature uniaxial accelerometer secured at the wrist. Electrogoniometer data were collected to determine the range of motion (ROM) as well as the angle between the forearm and band which was used to determine elastic moment arm. Paired t-tests were used to identify joint angle specific RJM differences between conditions. Results: Angle specific comparisons revealed that RJM in the moderate acceleration movement strategy was significantly different from RJM in the low acceleration movement strategy through 150° (83%) of range of motion (p<0.05). Shoulder RJM was up to 111% higher in the moderate acceleration strategy (P < 0.01). Angle specific comparisons revealed RJM in the <1:1 cadence strategy was significantly different from RJM in the 2:2 cadence through 108° (60%) of the range of motion (p<0.05). RJM was up to 47% higher in the <1:1 cadence (p<0.01). RJM in the low acceleration strategy was significantly greater with 30% elastic start strain relative to 0% elastic start strain through 180º of angular excursion (p<0.001). The pattern and magnitude of neuromuscular loading was significantly different in higher acceleration movement strategies (moderate acceleration and fast cadence). Conclusions: These findings indicate that differential limb acceleration as a result of movement strategy significantly affects shoulder load during elastic resistance exercise. The pattern and magnitude of load was different in each movement strategy and could result in differential neuromuscular adaptation through training. Clinicians and exercise professionals should consider movement strategy/acceleration as an important factor when prescribing elastic resistance exercise for safety and efficacy.

The purpose of this study was to compare the shoulder resultant joint moment (RJM) during a shoulder internal rotator exercise using elastic resistance employing four different movement strategies and two different starting elastic strains. Methods: Ten subjects aged 27.4 ± 2.6 yr (5 female and 5 male) with no previous shoulder pathology performed four sets of six repetitions of shoulder rotation though 180° using elastic resistance (Thera-Band® elastic band, blue) during two acceleration (medium and low) and two cadence (2s:2s, <1s:1s) strategies at 0% elastic starting strain. The acceleration movement strategies were also performed with starting strain of 30%. A mathematical model using Newtonian mechanics was used to compute the RJM. Elastic band recoil force was measured with a force transducer. Forearm acceleration was determined by a miniature uniaxial accelerometer secured at the wrist. Electrogoniometer data were collected to determine the range of motion (ROM) as well as the angle between the forearm and band which was used to determine elastic moment arm. Paired t-tests were used to identify joint angle specific RJM differences between conditions. Results: Angle specific comparisons revealed that RJM in the moderate acceleration movement strategy was significantly different from RJM in the low acceleration movement strategy through 150° (83%) of range of motion (p<0.05). Shoulder RJM was up to 111% higher in the moderate acceleration strategy (P < 0.01). Angle specific comparisons revealed RJM in the <1:1 cadence strategy was significantly different from RJM in the 2:2 cadence through 108° (60%) of the range of motion (p<0.05). RJM was up to 47% higher in the <1:1 cadence (p<0.01). RJM in the low acceleration strategy was significantly greater with 30% elastic start strain relative to 0% elastic start strain through 180º of angular excursion (p<0.001). The pattern and magnitude of neuromuscular loading was significantly different in higher acceleration movement strategies (moderate acceleration and fast cadence). Conclusions: These findings indicate that differential limb acceleration as a result of movement strategy significantly affects shoulder load during elastic resistance exercise. The pattern and magnitude of load was different in each movement strategy and could result in differential neuromuscular adaptation through training. Clinicians and exercise professionals should consider movement strategy/acceleration as an important factor when prescribing elastic resistance exercise for safety and efficacy.

In this dissertation we prove a version of the tropical Bezout's theorem which is applicable to all tropical projective plane curves. There is a version of tropical Bezout's theorem presented in other works which applies in special cases, but we provide a proof of the theorem for all tropical projective plane curves. We provide several different definitions of intersection multiplicity and show that they all agree. Finally, we will use a tropical resultant to determine the intersection multiplicity of points of intersection at infinite distance. Using these new definitions of intersection multiplicity we prove the complete tropical Bezout's theorem.

Contextualização: A compreensão das variáveis que modulam a sobrecarga externa oriunda dos exercícios de Pilates pode afetar as forças internas que agem na articulação do quadril e seu entendimento é de grande importância para os educadores físicos e fisioterapeutas que atuam nesse âmbito, que podem subsidiar a prescrição dos exercícios tanto para o treinamento físico quanto para a reabilitação. Objetivo: analisar o efeito da mola e da velocidade de execução de três exercícios de Pilates no comportamento e na magnitude da força muscular resultante (FMR) da articulação do quadril, obtida pela técnica de dinâmica inversa. Metodologia: 20 sujeitos praticantes de Pilates foram avaliados durante três exercícios de extensão de quadril com e sem mola: (1) leg lower mola alta (LLMA); (2) leg lower mola baixa (LLMB); (3) leg extension (LE). A partir da técnica da dinâmica inversa obtiveram-se os torques musculares e foram utilizando dados da literatura para quantificar a distância perpendicular média ponderada (DPMP) dos flexores e extensores de quadril e assim, estimar a FMR da articulação do quadril. A análise estatística utilizada foi uma ANOVA one-way para verificar o efeito principal dos exercícios sobre a FMR e uma correlação de Spearmann foi aplicada para descrever o comportamento da FMR ao longo de uma faixa de velocidade. Resultados: No exercício LE o esforço muscular passa de 200% do peso corporal, o LLMA atinge 50% e o LLMB, ao contrário dos demais exercícios, tem exigência da musculatura flexora nos últimos 10° da ADM. No LLMA, independente da velocidade a FMR foi a mesma. No LLMB, a FMR diminui com o aumento da velocidade. No LE, a FMR aumenta com o aumento da velocidade. Conclusão: Os diferentes exercícios de extensão de quadril apresentaram configurações distintas que interferiram na força muscular dos extensores de quadril. A velocidade de execução afeta de forma diferente cada um dos exercícios. / Background: Understanding of the behavior of external forces coming from the exercises can affect the internal forces that act in the hip joint and understanding is of great importance to the physical educators and clinical therapists that work in this field and can be helpful for prescribing exercises to physical training and rehabilitation. Objectives: To evaluate the effect of spring and the performing velocity of three exercises of Pilates in resultant muscle force (RMF) of the hip, with the support of inverse dynamics technique. Methods: Twenty Pilates practitioners, performed three hip extension exercises: (1) Leg Lower high spring (LLHS); (2) Leg Lower Low Spring (LLLS); (3) Leg extension (LE). From inverse dynamic technique the muscular moments were obtained and literature data was necessary to quantify the weighted mean moment arm (WMMA) of the hip flexors and extensors to estimate a RMF of the hip joint. The statistical analysis used was an ANOVA one way to verify the mean effect from the exercises on the RMF and Spearmann correlation was used to describe the RMF during different velocities. Results: In the exercise LE the muscular effort is greater than 200% of the body weight, in the LLHS was as high as 50% and the LLLS, contrary to the other exercises, have a flexors muscular effort in the last ten degrees of the range of motion. In the LLHS, independent of velocities the RMF is the same. In LLLS, the RMF decreases with the increase of velocity. In LE, the RMF increases with the increase of velocity. Conclusion: The different exercises of hip extension show singular configurations that alter in RMF of hip extensors. The performing velocity changes in different ways each exercises.

In 1955, Cassels proved a now celebrated theorem giving a search bound algorithm for determining whether a quadratic form has a nontrivial zero over the rationals. Since then, his work has been greatly generalized, but most of these newer techniques do not follow his original method of proof. In this thesis, we revisit his 1955 proof, modernize his tools and language, and use this machinery to prove more general theorems regarding height bounds for the common zeros of a system of polynomials in terms of the heights of those polynomials. We then use these theorems to give a short proof of a more general (albeit, known) version of Cassels' Theorem and give some weaker results concerning the rational points of a cubic or a pair of quadratics. / text

Contextualização: A compreensão das variáveis que modulam a sobrecarga externa oriunda dos exercícios de Pilates pode afetar as forças internas que agem na articulação do quadril e seu entendimento é de grande importância para os educadores físicos e fisioterapeutas que atuam nesse âmbito, que podem subsidiar a prescrição dos exercícios tanto para o treinamento físico quanto para a reabilitação. Objetivo: analisar o efeito da mola e da velocidade de execução de três exercícios de Pilates no comportamento e na magnitude da força muscular resultante (FMR) da articulação do quadril, obtida pela técnica de dinâmica inversa. Metodologia: 20 sujeitos praticantes de Pilates foram avaliados durante três exercícios de extensão de quadril com e sem mola: (1) leg lower mola alta (LLMA); (2) leg lower mola baixa (LLMB); (3) leg extension (LE). A partir da técnica da dinâmica inversa obtiveram-se os torques musculares e foram utilizando dados da literatura para quantificar a distância perpendicular média ponderada (DPMP) dos flexores e extensores de quadril e assim, estimar a FMR da articulação do quadril. A análise estatística utilizada foi uma ANOVA one-way para verificar o efeito principal dos exercícios sobre a FMR e uma correlação de Spearmann foi aplicada para descrever o comportamento da FMR ao longo de uma faixa de velocidade. Resultados: No exercício LE o esforço muscular passa de 200% do peso corporal, o LLMA atinge 50% e o LLMB, ao contrário dos demais exercícios, tem exigência da musculatura flexora nos últimos 10° da ADM. No LLMA, independente da velocidade a FMR foi a mesma. No LLMB, a FMR diminui com o aumento da velocidade. No LE, a FMR aumenta com o aumento da velocidade. Conclusão: Os diferentes exercícios de extensão de quadril apresentaram configurações distintas que interferiram na força muscular dos extensores de quadril. A velocidade de execução afeta de forma diferente cada um dos exercícios. / Background: Understanding of the behavior of external forces coming from the exercises can affect the internal forces that act in the hip joint and understanding is of great importance to the physical educators and clinical therapists that work in this field and can be helpful for prescribing exercises to physical training and rehabilitation. Objectives: To evaluate the effect of spring and the performing velocity of three exercises of Pilates in resultant muscle force (RMF) of the hip, with the support of inverse dynamics technique. Methods: Twenty Pilates practitioners, performed three hip extension exercises: (1) Leg Lower high spring (LLHS); (2) Leg Lower Low Spring (LLLS); (3) Leg extension (LE). From inverse dynamic technique the muscular moments were obtained and literature data was necessary to quantify the weighted mean moment arm (WMMA) of the hip flexors and extensors to estimate a RMF of the hip joint. The statistical analysis used was an ANOVA one way to verify the mean effect from the exercises on the RMF and Spearmann correlation was used to describe the RMF during different velocities. Results: In the exercise LE the muscular effort is greater than 200% of the body weight, in the LLHS was as high as 50% and the LLLS, contrary to the other exercises, have a flexors muscular effort in the last ten degrees of the range of motion. In the LLHS, independent of velocities the RMF is the same. In LLLS, the RMF decreases with the increase of velocity. In LE, the RMF increases with the increase of velocity. Conclusion: The different exercises of hip extension show singular configurations that alter in RMF of hip extensors. The performing velocity changes in different ways each exercises.

Introdução. O músculo esquelético se adapta a diferentes estímulos externos. Estas adaptações podem ser intrínsecas, bem como neurais, alterando a capacidade de produção de força. Portanto, é de se esperar que diferentes modalidades esportivas (ciclismo e triathlon), possuam diferentes adaptações intrínsecas e neuromusculares durante o ciclo de pedalada. O objetivo deste estudo foi investigar possíveis mudanças causadas pelo treinamento do ciclismo e do triathlon na arquitetura muscular, unidade músculo tendão, ativação muscular e suas possíveis consequências na capacidade de produção de força no pedal durante o ciclo de pedalada. Ainda, que efeitos o nível da carga de trabalho causa nas estruturas neuromusculares e capacidade de produção de força no pedal. Artigo I. A arquitetura muscular de ciclistas e triatletas não parece ter sido determinada. O presente estudo compara a arquitetura muscular, unidade músculo tendão, ativação muscular e forças no pedal entre ciclistas, triatletas e não-atletas ao longo do ciclo da pedalada. Os sujeitos realizaram um teste incremental para determinar a potência máxima. Forças no pedal, ativação muscular, cinemática articular e arquitetura muscular foram registradas na potência máxima correspondente a primeira sessão na cadência de 90 rpm. O maior ângulo de penação e menor comprimento de fascículo foram encontrados em ciclistas e triatletas, comparados a não-atletas (p < 0,05). Triatletas apresentam maior ativação do reto femoral que ciclistas e não-atletas (p < 0,05); e ciclistas tem maior ativação, comparados a não-atletas (p < 0,05). Triatletas e nãoatletas apresentam maior ativação do sóleo que ciclistas (p < 0,05) nos primeiros 90° do ciclo de pedalada, enquanto ciclistas ativam mais o sóleo que triatletas e não-atletas (p < 0,05) dos 90° aos 180° do ciclo de pedalada. Triatletas aplicam maior força resultante no pedal comparados a não-atletas no segundo quadrante, enquanto que no quarto quadrante não-atletas apresentam maior força resultante no pedal que ciclistas e triatletas (p < 0,05). O índice de efetividade é maior em ciclistas e triatletas, comparados a não atletas (p < 0,05). Ciclitas e triatletas são semelhantes na arquitetura muscular e forças no pedal, mas apresentam menor comprimento de fascículo e maior ângulo de penação, além de melhor eficiência das forças aplicadas ao pedal em relação a nãoatletas. Artigo II. Os efeitos da carga de trabalho na arquitetura muscular de ciclistas e triatletas ainda necessitam de melhores esclarecimentos. O objetivo deste estudo foi comparar a arquitetura muscular, unidade musculo-tendão, ativação muscular e forças no pedal em ciclistas, triatletas e não-atletas em diferentes níveis de carga de trabalho durante a fase propulsiva do ciclo de pedalada. Os participantes realizaram teste incremental para determinar o nível da carga de trabalho (máxima potência e potências correspondentes ao primeiro e segundo limiares ventilatórios). Forças no pedal, ativação muscular, cinemática articular e arquitetura muscular foram registrados um dia após a determinação dos respectivos níveis de carga de trabalho. Maior ângulo de penação e menor do comprimento de fascículo foram encontrados em ciclistas e triatletas, comparados a não-atletas (p < 0,05). A arquitetura muscular e a unidade músculotendão não sofreram alterações com o nível da carga de trabalho (p > 0,05). Ciclistas tem menor ativação do músculo vasto medial, comparados a triatletas e maior ativação do músculo sóleo comparados a triatletas e não-atletas (p < 0,05). Os músculos vasto medial, reto femoral, bíceps femoral e sóleo são mais ativados da com o incremento do nível da carga de trabalho (p < 0,05), sem alterações nos músculos tibial anterior e gastrocnêmio medial (p > 0,05). A força resultante e o índice de efetividade não diferem entre os grupos (p > 0,05). O incremento do nível da carga de trabalho aumenta a força resultante (p < 0,05) sem alterações no índice de efetividade (p > 0,05). Ciclistas e triatletas tem arquitetura muscular similar, mas diferem de não-atletas. O incremento da carga de trabalho, provoca aumento a ativação muscular e a força resultante. / Introduction. Skeletal muscle adapts to different external stimuli, and this adaptation can lead to intrinsic and neural changes, altering the capacity of the force produced. Therefore it is expected that different sports (cycling and triathlon) have different intrinsic and neuromuscular adaptations during crank cycle. Therefore, the objective of this study is to investigate possible changes caused to sports training (cycling and triathlon) in muscle architecture, muscle-tendon unit, muscle activation and its consequences in capacity of pedal force production in crank cycle. Furthermore, it is aimed at determining the effects of different effort levels on the muscle structures neural activation and pedal force mentioned above. Article I. Muscle architecture of cyclists and triathletes during pedaling is unknown. Our study compared muscle architecture, muscle-tendon unit and activation, and pedal forces of cyclists, triathletes and non-athletes during a complete crank cycle. Participants performed an incremental test to determine maximal power output. Pedal forces, muscle activation, joint kinematics and muscle architecture were recorded at maximal power output and 90 rpm of cadence. Increased pennation angle and shorter fascicle length were found for cyclists and triathletes compared to non-athletes (p < 0.05). Higher activation of rectus femoris for triathletes than cyclists and non-athletes (p < 0.05); and for cyclists compared to non-athletes were observed (p < 0.05). Triathletes and non-athletes had higher activation of soleus than cyclists (p < 0.05). Cyclists had higher soleus activation than triathletes and non-athletes (p < 0.05). Triathletes applied greater resultant force on the pedal compared to non-athletes in second quarter while non-athletes presented higher resultant force than triathletes and cyclists in fourth quarter (p < 0.05). The index of effectiveness was higher for the athletes compared to non-athletes (p < 0.05). Cyclists and triathletes were similar in terms of muscle architecture and pedal forces but presented increased in pennation angle and shorter fascicle length for cyclists and triathletes compared to non-athletes and better efficiency of the forces applied to the pedal in relation to non-athletes. Article II. Effects of workload level in cyclists and triathletes’ muscle architecture during pedalling is unknown. Our goal was to compare muscle architecture, muscletendon unit and activation, and pedal forces of cyclists, triathletes and non-athletes at different workload levels during the propulsive phase of the crank cycle. Participants performed an incremental test to determine workload level (maximal power output and power output of the first and second ventilatory thresholds). Pedal forces, muscle activation, joint kinematics and muscle architecture were recorded at pre-set workload level. Increased pennation angle and shorter fascicle length were found for cyclists and triathletes compared to non-athletes (p < 0.05). Muscle architecture and muscle-tendon unit length were not affected by workload level (p > 0.05). Cyclists achieved lower activation of vastus medialis compared to triathletes, and higher activation of soleus compared to triathletes and non-athletes (p < 0.05). Vastus medialis, rectus femoris, biceps femoris and soleus activations were increased at higher workload level for all groups (p < 0.05) without changes for tibialis anterior and gastrocnemius medialis (p > 0,05). Resultant force and effectiveness index did not differ for between groups (p > 0. 05). Higher workload level increased resultant force (p < 0.05) without changes in index of effectiveness (p > 0.05). Cyclists and triathletes were similar for muscle architecture but differed to non-athletes. Higher workload level increased muscle activation and resultant force.

Contextualização: A compreensão das variáveis que modulam a sobrecarga externa oriunda dos exercícios de Pilates pode afetar as forças internas que agem na articulação do quadril e seu entendimento é de grande importância para os educadores físicos e fisioterapeutas que atuam nesse âmbito, que podem subsidiar a prescrição dos exercícios tanto para o treinamento físico quanto para a reabilitação. Objetivo: analisar o efeito da mola e da velocidade de execução de três exercícios de Pilates no comportamento e na magnitude da força muscular resultante (FMR) da articulação do quadril, obtida pela técnica de dinâmica inversa. Metodologia: 20 sujeitos praticantes de Pilates foram avaliados durante três exercícios de extensão de quadril com e sem mola: (1) leg lower mola alta (LLMA); (2) leg lower mola baixa (LLMB); (3) leg extension (LE). A partir da técnica da dinâmica inversa obtiveram-se os torques musculares e foram utilizando dados da literatura para quantificar a distância perpendicular média ponderada (DPMP) dos flexores e extensores de quadril e assim, estimar a FMR da articulação do quadril. A análise estatística utilizada foi uma ANOVA one-way para verificar o efeito principal dos exercícios sobre a FMR e uma correlação de Spearmann foi aplicada para descrever o comportamento da FMR ao longo de uma faixa de velocidade. Resultados: No exercício LE o esforço muscular passa de 200% do peso corporal, o LLMA atinge 50% e o LLMB, ao contrário dos demais exercícios, tem exigência da musculatura flexora nos últimos 10° da ADM. No LLMA, independente da velocidade a FMR foi a mesma. No LLMB, a FMR diminui com o aumento da velocidade. No LE, a FMR aumenta com o aumento da velocidade. Conclusão: Os diferentes exercícios de extensão de quadril apresentaram configurações distintas que interferiram na força muscular dos extensores de quadril. A velocidade de execução afeta de forma diferente cada um dos exercícios. / Background: Understanding of the behavior of external forces coming from the exercises can affect the internal forces that act in the hip joint and understanding is of great importance to the physical educators and clinical therapists that work in this field and can be helpful for prescribing exercises to physical training and rehabilitation. Objectives: To evaluate the effect of spring and the performing velocity of three exercises of Pilates in resultant muscle force (RMF) of the hip, with the support of inverse dynamics technique. Methods: Twenty Pilates practitioners, performed three hip extension exercises: (1) Leg Lower high spring (LLHS); (2) Leg Lower Low Spring (LLLS); (3) Leg extension (LE). From inverse dynamic technique the muscular moments were obtained and literature data was necessary to quantify the weighted mean moment arm (WMMA) of the hip flexors and extensors to estimate a RMF of the hip joint. The statistical analysis used was an ANOVA one way to verify the mean effect from the exercises on the RMF and Spearmann correlation was used to describe the RMF during different velocities. Results: In the exercise LE the muscular effort is greater than 200% of the body weight, in the LLHS was as high as 50% and the LLLS, contrary to the other exercises, have a flexors muscular effort in the last ten degrees of the range of motion. In the LLHS, independent of velocities the RMF is the same. In LLLS, the RMF decreases with the increase of velocity. In LE, the RMF increases with the increase of velocity. Conclusion: The different exercises of hip extension show singular configurations that alter in RMF of hip extensors. The performing velocity changes in different ways each exercises.