Inverse dynamics

Inverse dynamics uses link-segment models to represent the mechanical behavior of connected pendulums, or more concretely, the limbs of humans, animals or robots, where given the kinematic representation of movement, inverse dynamics derives the kinetics responsible for that movement. In practice, from observations of the motion (of limbs), inverse dynamics is used to compute the associated moments (joint torques) that lead to that movement, under a special set of assumptions.

Applications

The fields of Robotics and Biomechanics constitute the major application areas for inverse dynamics.

In robotics, inverse dynamics algorithms are used to calculate the torques that a robot's motors must deliver to make the robot's end-point move in the way prescribed by its current task.

Similarly, the inverse dynamics in biomechanics describe what the muscles are doing, particularly the timing of their contractions, the amount of force generated to produce some moment about a joint, and the amount of mechanical work performed by that contraction. The resulting motion can be concentric or eccentric. Muscle kinematics describes these quantities in terms of Newtonian mechanics, specifically the Newton-Euler equations of:

: "Force equal mass times linear acceleration," and: "Moment equals mass moment of inertia times angular acceleration.

These equations mathematically model the behavior of a limb in terms of a knowledge domain-independent, link-segment model, such as an idealized skeleton with fixed-length limbs and perfect pivot joints. From these equations, Inverse dynamics derives the torque (moment) level at each joint based on the movement of the attached limb or limbs affected by the joint. This process used to derive the joint moments is known as inverse dynamics because it reverses the forward dynamics equations of motion, the set of differential equations which yield the position and angle trajectories of the idealized skeleton's limb from the accelerations and forces applied.

From joint moments, a biomechanist could infer muscle forces that would lead to those moments based on a model of bone and muscle attachments, etc, thereby estimating muscle activation from kinematic motion.

Correctly computing force (or moment) values from inverse dynamics can be challenging because external forces (e.g. ground contact forces) affect motion but are not directly observable from the kinematic motion. In addition, co-activation of muscles can leadto a family of solutions which are not distinguishable from the kinematic motion's characteristics.

ee also

* Kinematics
* Inverse kinematics: a problem similar to Inverse dynamics but with different goals and starting assumptions. While inverse dynamics asks for torques that produce a certain time-trajectory of positions and velocities, inverse kinematics only asks for a static set of joint angles such that a certain point (or a set of points) of the character (or robot) is positioned at a certain designated location. It is used in synthesizing the appearance of human motion, particularly in the field of video game design. Another use is in robotics, where joint angles of an arm must be calculated from the desired position of the end effector.

References

*cite book | author=Winter, D.A. | title=The biomechanics and motor control of human gait: normal, elderly and pathological | location=Waterloo, Ontario | publisher=University of Waterloo Press | year=1991 | id=

*cite journal | author=Kirtley, C.; Whittle, M.W; and Jefferson, RJ | title=Influence of Walking Speed on Gait Parameters | journal=Journal of Biomedical Engineering | year=1985 | volume=7(4) | pages=282–8 | doi=10.1016/0141-5425(85)90055-X

*cite journal | author=Jensen RK | title=Changes in segment inertia proportions between four and twenty years | journal=Journal of Biomechanics | year=1989 | volume=22(6-7) | pages=529–36

External links

* " [http://www.univie.ac.at/cga/teach-in/inverse-dynamics.html Inverse dyanamics] " Chris Kirtley's research roundup and tutorials on biomechanical aspects of human gait.

* " [http://cmr.utk.edu Center for Musculoskeletal Research] " Advanced research laboratory at the forefront of inverse dynamics, forward dynamics, and all aspects of biomechanics.