Inverse Dynamics Flashcards
Inverse Dynamics
- Previous calculations have required the assumption of equilibrium
- calculate loads within the body when the body is not in equilibrium = there is acceleration = have linear + generally angular acceleration
- Dynamics: can be used to analyse moving objects using Newton’s second law
- Inverse dynamics: use external forces that result from muscle contractions, + use these to go back + work out what muscle actions must have been present
○ The greater the joint torque, the greater the net muscle contraction
Newton’s second law
Forward dynamics: a = ∑F / m
Inverse dynamics: ∑F = m x a
= not simulating the system, the system is already running = + we are trying to work out what the forces are
Moment of Inertia
- The moment of inertia of an object determines its resistance to angular acceleration.
- Large moment of inertia means object is difficult to accelerate
- Mass is one component = so is the distribution of those mass elements from the axis of rotation
- Moment of inertia is dependent upon the axis of rotation
Radius of Gyration
- Radius of Gyration is the distance from the axis of rotation to a point where the body’s mass could be concentrated, without altering its rotational characteristics
- I = mk2
- Radius of Gyration is not the distance to the centre of mass
Radius of Gyration cont
- For linear kinetics, we pretend all the mass is concentrated at the centre of mass
- For angular kinetics, we pretend all the mass is located at a point at a distance k from the axis of rotation
○ Linear kinetics = have COM
○ Angular kinetics = are using moment of inertia so can’t use COM = so use radius of gyration number to help calculate moment of inertia - Radius of gyration is reported in anthropometric tables
Anthropometric Data
- Tables generally represent data from elderly populations
- Tables not specific to younger pops = that are say performing sport
- Easy to implement in computer programs
- 3D body scanning technology more accurate, but time consuming + expensive
IMPORTANT NOTE
Important Note!
* When calculating the torques for an object not in equilibrium, the torques MUST be summed around the COM
* Therefore, forces must be calculated before torques, because the joint reaction forces exert a torque about the centre of mass
Assumptions inherent in the Inverse Dynamics Method
- Each segment has a fixed mass located as a point mass at its COM (which will be the centre of gravity in the vertical direction).
- The location of each segment’s COM remains fixed during the movt
- The joints are considered to be hinge (or ball + socket) joints.
- The mass MOI of each segment about its mass centre is constant during the movt.
- The length of each segment remains constant during the movt (e.g., the distance b/w hinge or ball + socket joints remains constant)
- Can the process be continued through the body to calculate shoulder torques?
- If not, why not?
○ One problem = using a rigid body assumption + the belly + the thorax aren’t so rigid
○ Second thing = as go up through the model = the foot is probably modeled most accurately except for the fact you can argue it should be 2 or 3 segments = as go up there are small errors + these errors keep being multiplied as go up the chain so by the time you get to the shoulder = would still have more errors
- If not, how would we calculate shoulder torques?
○ Start from hand + move up the arm
Summary of Inverse Dynamics
- Newton’s second law used to calculate unknown forces + torques within a single rigid segment.
- Simplifications to the model reduce the number of unknown’s but at the expense of loss of info
- Net muscle torque can be calculated across a joint, not partitioned into separate muscles = can’t tell you how active each muscle is or how efficient the contraction is either
○ Can’t even distinguish b/w co-contractions around a joint - Calculated joint force is the sum of all muscle AND joint forces added together.
- Inverse dynamics calculations are performed for a single instant in time.
- If taking measurements 100 times per sec, calculations must be repeated 100 times per sec
- requires use of computers.
Summary of Inverse Dynamics CONT
- Inverse dynamics methods have significant limitations reducing the amount we can learn.
○ Cannot separate muscle/ tendon / joint reaction forces
○ Therefore, cannot know what loading is within a joint
○ Only get net torque, not individual muscle groups - Only way to estimate these indiv forces is w/ complex model estimating forces in indiv muscles
- Linked segment model is better than nothing
○ Without the simplifications, would not have joint torques either
