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Reverse Abdomen Crunches – Biomechanics

Reverse abdominal crunches are widely practiced in fitness training. Many people want to do this exercise to reduce the size of their waist without knowing if they are qualified to do this exercise (because the unqualified people invite injuries to the back).

Reverse abdominal curls are done by raising both legs at the same time, keeping them straight. About 32% of the total body weight is contributed by the lower limbs (This figure is approximate according to Williams and Lissner, 1962. Video: Textbook: Basic Biomechanics explained by John Low & Ann reed). We will take an example of a person who weighs 100 kg. When this person tries to do a reverse sit-up (straight leg raise), he has to lift legs that weigh around 32 kg. Straight leg raise is a bilateral flexion of the legs and hip flexion agonist is the Ilio-psoas muscle. But to prevent knee flexion due to the effect of gravity, Quadriceps should also work. The role of the abdominal muscle is to stabilize the proximal attachment points of the Ilio-psoas (and Quadriceps as well), i.e. the vertebrae and pelvis. If the abdominal muscles are unable to stabilize the vertebrae and pelvis, lumbar lordosis inevitably occurs. In fact, the challenge of the abdominal inversion exercise is not only to lift the legs, but also to strictly ensure the ‘stabilizing’ function of the abdominal muscles.

To understand the amount of gravitational torque acting on the hip joints during a reverse abdominal squat, one must know how to predict the ‘Part’s Center of Gravity’ of the lower limbs. The fractional center of gravity of the lower legs may be just above the knee joint, as the thigh contributes 10% of the total body weight, the foot contributes 4.5% of the total body weight, and the foot contributes 1.5% of the total body weight. based on Williams and Lissner). Gravity tends to act on a part’s center of gravity. To calculate the amount of gravitational torque (GT), various factors such as (a) muscle effort arm (b) muscle step arm (c) resistance arm (d) lower leg mass, are taken into account. Except for the moment arm of the muscle, the value of all other factors can be predicted.

Let’s assume that the length of the lower legs of this 100 kg person is 90 cm (hip to bottom). We can also assume that the center of gravity of the lower legs is 40 cm from the hip joint and the ilio-psoas muscle is attached to the lesser trochanter 10 cm from the hip joint.

Right now;

1. Effort arm = 10 cm (distance between hip joint and ilio-psoas insertion point)

2. Arm of resistance = 40 cm (distance between hip joint and center of gravity)

3. Lower leg mass = 32 kg (16 kg per leg)

Gravitational Torque (GT) = [mass x acceleration due to gravity] x resistance arm in meters

= [32 kg x 9.8 ms-2] x 0.4 m

= 125 Nm

Anti-gravitational torque (AGT) = GT / Force arm in meters

= 125 Nm / 0.1 m

= 1250 Newtons

(Note: AGT must be produced by the Ilio-psoas muscle. Each Ilio-psoas muscle must produce more than 625 Newtons to cause a straight leg lift).

To prevent lumbar lordosis, the abdominal muscles must also produce more than 1250 Newtons to stabilize the lumbo-pelvic unit. This high power requirement for AGT production is also necessary in the initial few degrees of leg lift because as the angle of lift increases, the resistance arm of the weight decreases. Therefore, the AGT requirement is directly related to the ‘variable resistance weapon’. We need to insert another factor (cosine θ) into the formula to calculate AGT as follows;

AGT = GT x cosine θ / Arm of effort in meters

Where, Θ – denotes the angle between the raised legs and the ground

Just having two examples, let us understand that (a) anti-gravitational torque (b) anti-gravitational torque (b) anti-gravitational torque decreases.

Example: 1 (angle between raised legs and the floor = 30 degrees)

Anti-gravity torque = 125 x cosine of 30 degrees/mile of effort in meters

= (125 x 0.866) / 0.1 m

= 1082.5 Newtons

Example: 2 (angle between raised legs and floor = 60 degrees)

Anti-gravity torque = 125 x cosine 60 degrees / Arm of effort in meters

= (125 x 0.5) / 0.1 m

= 625 Newtons

These analyzes clearly show that the closer the feet are to the ground (a) the greater the GT (b) the greater the AGT (c) the greater the stabilizing role of the abdomen (d) the greater the magnitude of the lumbar lordosis if the abdominal muscles are sufficient They are not strong. Only those who have the ability to control lumbar lordosis in the initial few degrees of leg elevation can be described as eligible for reverse abdominal amputation. Incompetent individuals, who are unable to control lumbar lordosis in the initial few degrees of leg elevation, can invite unnecessary injuries.

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