How many positions to train through full range of motion?

Disclaimer : This information is not guaranteed to be accurate and I am not liable if you make any decisions or take any actions, in terms of medical treatment, health decisions, exercise, behavior or anything else based on the information presented. I am not telling you any decisions to make even if I use terms like "you" but am using the word "you" as part of a writing style to simplify writing. Any suggestions for what "you" should do are not for you personally to do but what someone might do as part of a exercise or nutrition program which might help some people's health and make other people's health worse. You should not do any activity that will make your health worse even if "you" should do it according to the program described. If the information is wrong and you believe it is true, act on it and it causes you problems, I am not responsible because I have warned you the information is not guaranteed to be accurate.

This is a theoritical framework not an exercise prescription and not all exercises presented may be safe for all individuals

Theoritical number of isometric exercises to strength train a joint in all 3 planes through a full range of motion

Without considering multiple joint muscles

If you need to train a joint isometrically in positions every 15 degrees through a 360 degree range of motion in each of 3 planes resisting force in each of six directions based on three perpendicular translations and their opposites

For all single joint muscles for that one joint

= ( 360 / 15 ) * ( 360 / 15 ) * ( 360 / 15 ) * 6 = 82944

= ( 360 / 15 ) ^ 3 ) * 6

Considering multiple joint muscles

For all two joint muscles for one joint with one joint proximal to it and one joint distal to it.

Joint A is proximal to joint B and joint C is distal to joint B and joint B is between joint A and C. Joint A, B and C all have 360 degree range of motion in all 3 planes.

For training two joint muscles that are for A and B plus training two joint muscles that are for B and C

= [ ( ( 360 / 15 ) ^ 6 ) * 6 ] + [ ( ( 360 / 15 ) ^ 6 ) * 6 ]

= 2 * ( ( 360 / 15 ) ^ 6 ) * 6 = 2293235712

Training every 15 degrees in all combinations of all three planes resisting 6 directions of force is unrealistic, just training at the end range of motion against 2 directions of force has less combinations.

Training every 15 degrees is unrealistic so what about just training at the end range of motion and only resisting two forces passive resistance against a force trying to push you further into that direction and active resistance against a force trying to prevent you from moving further in that direction.

How many exercises are practical to train shoulder internal and external rotation

For isometrically training the shoulder in maximum internal and maximum external rotation with the vector from the proximal end of the humerous to the distal end of the humerous pointing in all three orthogonal translations and their opposites resisting a force trying to either rotate the humerus farther or in the opposite direction trying to undo the rotation effort with the elbow bent at 90 degrees

= 7 * 2 * 2 = 28

but in practical reality

= 5 * 2 * 2 = 20

seven not six because the humerus vector points in approximately the same direction in maximum horizontal abduction or horizontal flexion should be the same position as maximum horizontal adduction or horizontal extension but those two different ways to get to approximately the same direction work different muscle groups and are both blocked from reaching the same direction by the torso. But in practical reality most people can only have their hunerus point in five of the six directions

Description of list parameters

This list is for the right shoulder joint relative to the anatomical position

To understand this list on the left shoulder switch the words left and right

Long description of each section of items on the list as separated by commas

The direction the vector from the proximal to the distal end of the radius would point, the shoulder would flex, extend, adduct or abduct in the transverse, sagital or coronal plane, the humerous would internally or externally rotate along the long axis of the humerus or the shoulder would internally or externally rotate, this is possible or impossible without assistance by an outside force to get approximately into that position for most people

Short description of each section of items on the list as separated by commas

Direction humerus vector points, how to get there from anatomical position, strength train internal or external rotation, level of plausibility as exercise for most people of typical flexibility

The list for isometric strength training

1 Translate forward, flex in the sagital plane 90 degrees, internally rotate, possible

2 Translate forward, extend in the sagital plane 90 degrees, externally rotate, possible

3 Translate backward, extend in the sagital plane 90 degrees, internally rotate, possible

4 Translate backward, extend in the sagital plane 90 degrees, externally rotate, possible

5 Translate up, abduct in the coronal plane 180 degrees or flex in the sagital plane 180 degrees, internally rotate, possible

6 Translate up, abduct in the coronal plane 180 degrees or flex in the sagital plane 180 degrees, externally rotate, possible

7 Translate down, starting in anatomical position, internally rotate possible

8 Translate down, starting in anatomical position, externally rotate possible

9 Translate right, abduct in the coronal plane 90 degrees, internally rotate, possible

10 Translate right, abduct in the coronal plane 90 degrees, externally rotate, possible

11 Translate left, adduct in transverse plane 90 degrees after flexing in the sagital plane 90 degrees, internally rotate, impossible

12 Translate left, adduct in transverse plane 90 degrees after flexing in the sagital plane 90 degrees, internally rotate, impossible

13 Translate left, abduct in transverse plane 90 degrees after extending in the sagital plane 90 degrees, internally rotate, extremely impossible

14 Translate left, abduct in transverse plane 90 degrees after extending in the sagital plane 90 degrees, internally rotate, extremely impossible

Double the number of items on the list to include two directions of force for isometric strength training

Active resistance against a force trying to prevent internal rotation for an internally rotated shoulder in active insufficiency

Active resistance against a force trying to prevent external rotation for an externally rotated shoulder in active insufficiency

Passive resistance against a force trying to prevent internal rotation for an internally rotated shoulder in passive insufficiency

Passive resistance against a force trying to prevent external rotation for an externally rotated shoulder in passive insufficiency

A shorter list for with concentric and eccentric strength training

This list of 5 possible items includes 10 possible exercises because each exercise has two parts to it based on force from two opposite directions. There are two ways to do each of the exercises and because the torque has different minimums and maximums for each of the two ways it would make sense to alternate which way is chosen. 2 items include 4 exercises that are not reasonably possible for most people.

1 Translate forward, flex in the sagital plane 90 degrees, alternate between internally and externally rotating

Possibility A

Split into two exercises resistance against an up force and resistance against a down force each for the full range of motion. This maximizes torque in the middle range of motion and minimizes it in the end range of motion.

Possibility B

Split into two exercises resistance against a force to the right and resistance against a force to the left each for the full range of motion. This maximizes torque in the end range of motion and minimizes the torque in the middle range of motion.

2 Translate backward, extend in the sagital plane 90 degrees, alternate between internally and externally rotating

Possibility A

Possibility B

3 Translate up, abduct in the coronal plane 180 degrees or flex in the sagital plane 180 degrees, alternate between internally and externally rotating

Possibility A

Possibility B

Split into two exercises resistance against a forward force and resistance against a backward force each for the full range of motion. This maximizes torque in the middle range of motion and minimizes it in the end range of motion.

4 Translate down, starting in anatomical position, alternate between internally and externally rotating.

Possibility A

Split into two exercises resistance against a force to the right and resistance against a force to the left each for the full range of motion. This maximizes torque in the middle range of motion and minimizes it in the end range of motion.

Possibility B

Split into two exercises resistance against a forward force and resistance against a backward force each for the full range of motion. This maximizes torque in the end range of motion and minimizes the torque in the middle range of motion.

5 Translate right, abduct in the coronal plane 90 degrees, alternate between internally and externally rotating, possible

Possibility A

Possibility B

6 Translate left, adduct in transverse plane 90 degrees

Translate left, abduct in transverse plane 90 degrees after extending in the sagital plane 90 degrees, alternate between internally and externally rotating

Impossibility A

Impossibility B

7 Translate left, abduct in transverse plane 90 degrees after extending in the sagital plane 90 degrees, alternate between internally and externally rotating, extremely impossible

Impossibility A

Impossibility B

Estimate for amount of strength training missed out on by only training with the humerus pointed in 6 directions

I would guess that by training every 90 degrees in the cases described above one would in the worst case scenario have their maximum strength divided by the square root of 2 for any position that is between two of the 90 degree positions and 45 degrees apart from both of them. Where, the force that is divided by the square root of 2 is the weaker one of each of the two positions it is in between

How many strength training exercises for a joint ignoring multijoint muscles and internal and external rotation and only resisting two force directions

For ignoring multi joint muscles and ignoring internal and external rotation and strengthening the hip or shoulder at maximum range of motion against a force and it's opposite either trying to push the range of motion beyond the maximum or prevent the range of motion from reaching it's maximum

= 3 * 2 * 2 = 12

Maximum flexion and extension in the sagital plane

Maximum adduction and abduction in the frontal or coronal plane

Maximum horizontal flexion or adduction and extension or abduction in the transverse plane

Doubling or halving the list for both sides or for only one direction of force

Remember that is for one hip or one shoulder to do both hips or both shoulders the amount of time would be doubled if you do one joint at a time and halved if you only work the force in one direction instead of two.

Someone might for example only want to do active sufficiency strength training and not do passive sufficiency strength training which would half the time.

In some cases you can train also train both hips or both shoulders at the same time and half the time, although this is not always possible or adviseable. You can not adduct both hip joints or both shoulder joints at the same time through full range of motion either in the transverse or corinal plane because body parts will block one another. It might work different muscle groups to flex both hips simultaneously than to flex each hip individually so although it is possible it might not be adviseable to split time in half that way every time someone exercises. It might be better to sometimes flex both the hips at the same time and other times do each hip separately.

Ideal exercises for hip in sagital plane considering multi joint interactions in order to achieve passive or active insufficiency of sagital plane hip flexing or extending muscles

By ideal I mean theoritically what type of exercises would achieve that type of goal

Hip Flexion in the sagital plane

Flex hip in sagital plane, straighten knee or extend knee in sagital plane, torso should be straight or forward bending or flexed in sagital plane. Someone would need to continue to bend their torso forward or flex their hip further until they can not do either one any further in order to achieve active or passive insuffiency.

Active or passive insufficiency depends on direction of force resisted

From this position you can achieve active insufficiency of hip flexing muscles or passive insufficiency of hip extending muscles depending on the direction of force isometrically resisted.

Mutiple combinations of hip flexion vs torso forward bending

There is more than one combination of this because someone can do this because someone can do this with a relative increase in forward bending of the torso but relatively reduced hip flexion or with a relative decrease in forward bending of the torso and relative increase in hip flexion. Higher priority should be taken in bending the lower sections of the torso over the higher sections of the torso if one is to achieve hip muscle active or passive insufficiency.

Bipassing the limit in which the legs can not pass through the torso

I am not using an anatomical definition of the leg that excludes the bone and flesh above the knee but a normal definition of the leg in this paragraph. This can be done one legged or symetrically done with two legs. If done with one leg the leg that is not flexing at the hip joint can be neutral at 0 degrees extension in the sagital plane or can be extended backward in the sagital plane but should not be flexed forward in the sagital plane. When doing this symetrically with two legs there is a maximum that can be reached if the hips are neutral in the coronal plane with 0 degrees of adduction or which the hips are maximally adducted in the coronal plane and the knees and or ankles are touching because the torso can not pass through the legs in such a situation. But, this can be bipassed by abducting the hips the minimum amount for the torso to pass through. When doing this with one leg there is a maximum that can be reached if someone's hip is neutral with 0 degrees in the coronal plane or is adducted more than 0 degrees in the coronal plane because the torso can not pass through the legs in such a situation. But, this can be bipassed by abducting the hip the minimum amount for the torso to pass through.

Hip extension in the sagital plane

Extend hip in sagital plane, bend knee or flex knee in sagital plane, torso should be straight or backward bending or extended in sagital plane. Someone would need to continue to bend their torso backward or extend their hip further until they can not do either one any further in order to achieve active or passive insuffiency.

Active or passive insufficiency depends on direction of force resisted

From this position you can achieve active insufficiency of hip extending muscles or passive insufficiency of hip flexing muscles depending on the direction of force isometrically resisted

Mutiple combinations of hip extension vs torso backward bending

There is more than one combination of this because someone can do this because someone can do this with a relative increase in back bending of the torso but relatively reduced hip extension or with a relative decrease in back bending of the torso and relative increase in hip extension. A relative increase in flexing or bending of the knee might also result in a relative decrease in back bending of the torso and or hip extension. Higher priority should be taken in bending the lower sections of the torso over the higher sections of the torso if one is to achieve hip muscle active or passive insufficiency.

Bipassing the limit in which the legs can not pass through the torso

I am not using an anatomical definition of the leg that excludes the bone and flesh above the knee but a normal definition of the leg in this paragraph. This can be done one legged or symetrically done with two legs. If done with one leg the leg that is not extending at the hip joint can be neutral at 0 degrees flexion in the sagital plane or can be flexed forward in the sagital plane but should not be extended backward in the sagital plane. When doing this symetrically with two legs there is a maximum that can be reached if the hips are neutral in the coronal plane with 0 degrees of adduction or which the hips are maximally adducted in the coronal plane and the knees and or ankles are touching because the torso can not pass through the legs or feet in such a situation. But, this can be bipassed by abducting and or internally rotating the hips the minimum amount for the torso to pass through. When doing this with one leg there is a maximum that can be reached if someone's hip is neutral with 0 degrees in the coronal plane or is adducted more than 0 degrees in the coronal plane because the torso can not pass through the legs in such a situation. But, this can be bipassed by abducting the hip the minimum amount for the torso to pass through.

Why internal rotation and a warning to minimize internal rotation

The internal rotation may be necessary because if the knee or knees are bent the torso might be blocked by the foot or feet or lower leg or legs in a manner it would not be blocked if the knee or knees are straight and only abduction would be necessary. It is probably safer or less dangerous to abduct more and internally rotate less instead of internally rotating more and abducting less.

Active or passive insuffiency of the coronal plane hip adductor or abductor muscle groups during coronal plane hip abduction of only one right leg

Right vs left

To understand how to do this on the left leg switch the words left and right

Meaning of leg

I am not using an anatomical definition of the leg that excludes the bone and flesh above the knee but a normal definition of the leg in this section

One legged assumption

I am assuming one of the two legs has the knee straight or almost straight and is in anatomically neutral position or in neutral position except possibly internally or externally rotated. That hip is not flexed or extended in the sagital plane and the hip is not adducted or abducted in the coronal nor transverse plane.

Lying on side or standing

The individual would be standing or lying on their left side. If standing then their standing leg's knee would either be straight or almost straight. If lying on the side the leg, I will assume the leg that is not engaging in coronal plane abduction has a straight knee.

The torso

For one legged hip abduction of the right hip the torso should be straight or lean or bend to the right in the sagital plane in order to achieve active or passive insufficiency

My guesses concerning the knee of the working leg and internal or external rotation of the hip of the working leg

If the hip is externally rotated such that the toes would be pointed up or superiorly if the person would be standing on the other leg or are in a similar position but lying down. My guess would be straightening the knee would help achieve active or passive insufficiency of some coronal plane hip adductors or abductors and bending the knee might prevent active or passive insufficiency or some coronal plane hip adductors or abductors.

If the hip is in neutral and not externally or internally rotated such that if the knees were straight the toes would be pointed forward or anteriorly if the person would be standing on the other leg or in a similar position lying down. My guess would be that maximally flexing or bending the knee would put one group of coronal plane hip adductors in passive or active insufficiency and maximally straightening or extending the knee would put a different group of coronal plane hip adductors in passive or active insufficiency.

Which way should the hip be rotated for safety

If one is training at passive insufficiency resisting a force pushing the foot up in a direction to cause further hip abduction in the coronal plane or if one is training at active insufficiency resisting a force pushing the foot down in a direction to cause prevent hip abduction in the coronal plane. Then it might be safer to have hip externally rotated in the position where the toes would be pointed up or superiorly if one was standing on one leg or in a similar position while lying down. The reason would be so that the knees are not resisting a force that would produce a torque perpendicular to the direction they normally bend. One could instead have a force applied forward or backward anteriorly or posteriorly against the feet if the hips were not externally rotated and were in the other position I described but then the exercise would no longer primarily target for work the coronal plane hip adductors or abductors and instead target the transverse plane hip adductors or abductors.

Active or passive insuffiency of the coronal plane hip adductor or abductor muscle groups during coronal plane hip adduction of only one right leg

Active or passive insuffiency of the transverse plane hip adductor or abductor muscle groups during coronal plane hip abduction of only one right leg

Active or passive insuffiency of the transverse plane hip adductor or abductor muscle groups during coronal plane hip adduction of only one right leg

Torso Forward Bend

Torso Back Bend

Torso clockwise and counterclockwise twists

Torso left and right side bends

Neck Forward Bend

Neck Back Bend

Neck clockwise and counterclockwise twists

Neck left and right side bends

Other muscle groups, joints or body part locations which may be much more difficult to figure out how many exercise combinations there would be at a minimum to target all muscles for active and passive insufficiency

Shoulder, Elbow and Forearm

Something as simple as choosing whether or not you pronate or supinate the forearm effects whether or not you target the biceps when flexing the elbow but the biceps also work at the shoulder

Something as simple as the elbow joint that is often thought of as only bending in one plane like a hinge joint may actually be complicated to work all the muscle groups with

Pronated or Supinated forearm (2)

Bent or extended elbow (2)

Internally or externally rotated or neutral shoulder (3)

Translational positions the humerus can point, all but one of 3 perpendicular translations and there opposites as described earlier (5)

2*2*3*5 = 60 potential exercise combinations for active insufficiency

120 potential exercise combinations for active or passive insufficiency

Elbow, Forearm, Wrist, Hand and Fingers ignoring thumb

Wrist flexed or Extended or neutral (3)

Wrist ulnar or radially deviated or neutral (3)

Forearm Supinated or Pronated (2)

Elbow flexed or extended (2)

Fingers flexed or extended / straight (2)

3 * 3 * 2 * 2 * 2 = 72 potential exercise combinations for active insufficiency

144 potential exercise combinations for active or passive insufficiency

Hip, Knee, Upper Leg (thigh) and Lower Leg excluding feet

120 if similar to Shoulder, Elbow and Forearm

Leg at Knee height and below, Ankle, Feet and Toe

144 if similar to Elbow, Forearms, Wrists, Hands and Fingers ignoring thumb

Neck and Shoulders

Bending the neck to the left or right side in the coronal plane may effect if the shoulder muscles are in active or passive insufficiency when they are being adducted or abducted in the coronal plane

Head, Mouth, Jaw and Face muscles

Jaw opening or closing may interact with neck exercises to influence whether or not muscles are at active or passive insufficiency

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How many positions to train through full range of motion?

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