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visual3d:documentation:kinematics_and_kinetics:inverse_dynamics [2024/07/16 19:25] – created sgrangervisual3d:documentation:kinematics_and_kinetics:inverse_dynamics [2024/11/20 17:04] (current) – [Inverse Dynamics Calculations in Visual3D] wikisysop
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-====== Inverse_Dynamics ======+====== Inverse Dynamics ======
  
 Kinetics refers to the calculation of the Joint Moment and Joint Force. All other Kinetic signals are derived from the moment, force, and kinematic data. Kinetics refers to the calculation of the Joint Moment and Joint Force. All other Kinetic signals are derived from the moment, force, and kinematic data.
  
 Inverse Dynamic calculations are usually represented by [[Visual3D:Documentation:Visual3D_Signal_Types:LINK_MODEL_BASED_Data_Type|Model_Based_Items]]. Inverse Dynamic calculations are usually represented by [[Visual3D:Documentation:Visual3D_Signal_Types:LINK_MODEL_BASED_Data_Type|Model_Based_Items]].
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-=== Inverse Dynamics === 
  
 Biomechanical movement analysis provides a quantitative record of motion, and thereby allows objective comparison of performance across different conditions and patient groups. Biomechanical movement analysis typically involves several discrete steps. First, the motion of tracking targets attached to the subject is recorded using cameras. Second, a biomechanical model is defined to represent selected characteristics of the subject such as the number and type of segments (inertial properties), the joint properties (number of degrees-of-freedom (dof)), and the kinds of actuators that move the segments. Third, the kinematics of the model are calculated by determining the transformation from recorded tracking markers to the pose of each segment of the biomechanical model. The definition of the biomechanical model can be a crucial determinant of the reliability of the transformation between tracking markers and model pose and for interpreting specific movement disorders. Fourth, inverse dynamics analysis is applied to the kinematics of the biomechanical model and to the location, magnitude, and direction of externally applied forces (e.g., ground reaction forces acting on the foot). Biomechanical movement analysis provides a quantitative record of motion, and thereby allows objective comparison of performance across different conditions and patient groups. Biomechanical movement analysis typically involves several discrete steps. First, the motion of tracking targets attached to the subject is recorded using cameras. Second, a biomechanical model is defined to represent selected characteristics of the subject such as the number and type of segments (inertial properties), the joint properties (number of degrees-of-freedom (dof)), and the kinds of actuators that move the segments. Third, the kinematics of the model are calculated by determining the transformation from recorded tracking markers to the pose of each segment of the biomechanical model. The definition of the biomechanical model can be a crucial determinant of the reliability of the transformation between tracking markers and model pose and for interpreting specific movement disorders. Fourth, inverse dynamics analysis is applied to the kinematics of the biomechanical model and to the location, magnitude, and direction of externally applied forces (e.g., ground reaction forces acting on the foot).
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 A free body diagram of two segments, showing the traditional assumptions for inverse dynamics analysis. A free body diagram of two segments, showing the traditional assumptions for inverse dynamics analysis.
  
-{{JointForce.gif}}\\+{{:JointForce.gif}}\\
  
  
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 In [[Visual3D:Documentation:Kinematics_and_Kinetics:Six_Degrees_of_Freedom|6 DOF]] tracking there is no explicit linkage (or joint) connecting the segments. Visual3D explores the collection of segments and considers any two segments in proximity (the distal end of one segment and the proximal end of another segment within the radius of the segment ends) to be "linked" and references a **//Joint//** between them. The **//Joint//** does not constrain the segments, but is rather a bookkeeping tool that keeps track of which segments are assumed to have an equal and opposite Joint Reaction Force acting between their endpoints and an equal and opposite Joint Moments acting on the adjacent segments. In [[Visual3D:Documentation:Kinematics_and_Kinetics:Six_Degrees_of_Freedom|6 DOF]] tracking there is no explicit linkage (or joint) connecting the segments. Visual3D explores the collection of segments and considers any two segments in proximity (the distal end of one segment and the proximal end of another segment within the radius of the segment ends) to be "linked" and references a **//Joint//** between them. The **//Joint//** does not constrain the segments, but is rather a bookkeeping tool that keeps track of which segments are assumed to have an equal and opposite Joint Reaction Force acting between their endpoints and an equal and opposite Joint Moments acting on the adjacent segments.
  
-=== Inverse Dynamics Calculations in Visual3D ===+====== Inverse Dynamics Calculations in Visual3D ======
  
 Kinetics is the study of the forces and moments that cause motion of a body. For human movement, biomechanics attempt to determine the forces that result from muscle contractions and the torques that are produced, which together bring about the movement of the segments and thus of the whole body. Kinetics is the study of the forces and moments that cause motion of a body. For human movement, biomechanics attempt to determine the forces that result from muscle contractions and the torques that are produced, which together bring about the movement of the segments and thus of the whole body.
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 Visual3D's inverse dynamics calculations are implemented using the following recursive scheme. One of the features of the inverse dynamics algorithms is that it is straightforward to add external forces and torques to any segment. Visual3D's inverse dynamics calculations are implemented using the following recursive scheme. One of the features of the inverse dynamics algorithms is that it is straightforward to add external forces and torques to any segment.
  
-{{EquationsOfMotion1.gif}}\\+{{:EquationsOfMotion1.gif}}\\
  
  
 The Proximal Joint Reaction force is computed in the Global Coordinate System. The segments attached distally to any segment are identified (e.g. for a conventional lower body gait analysis the pelvis segment as two distal chains comprising a thigh, shank, and foot segment. An iterative algorithm for the proximal joint force, which allows any applied external force on segments is: The Proximal Joint Reaction force is computed in the Global Coordinate System. The segments attached distally to any segment are identified (e.g. for a conventional lower body gait analysis the pelvis segment as two distal chains comprising a thigh, shank, and foot segment. An iterative algorithm for the proximal joint force, which allows any applied external force on segments is:
  
-{{EquationsOfMotion2.gif}}\\+{{:EquationsOfMotion2.gif}}\\
  
  
 The Proximal Couple (moment) computed at the proximal end of a segment is computed in a segment (local) coordinate system: The Proximal Couple (moment) computed at the proximal end of a segment is computed in a segment (local) coordinate system:
  
-{{EquationsOfMotion3.gif}}\\+{{:EquationsOfMotion3.gif}}\\
  
  
 Transform the inertial torque from the Segment Coordinate System into the Global (Laboratory) Coordinate System using a transformation matris that is computed from the motion capture data. Transform the inertial torque from the Segment Coordinate System into the Global (Laboratory) Coordinate System using a transformation matris that is computed from the motion capture data.
  
-{{EquationsOfMotion4.gif}}\\+{{:EquationsOfMotion4.gif}}\\
  
  
 The Couple acting on a segment due to the inertial terms is: The Couple acting on a segment due to the inertial terms is:
  
-{{EquationsOfMotion5.gif}}\\+{{:EquationsOfMotion5.gif}}\\
  
  
 Expanding the Force terms and reducing the resulting equation yields the proximal moment due to the inertial forces and applied moments at the joint. Expanding the Force terms and reducing the resulting equation yields the proximal moment due to the inertial forces and applied moments at the joint.
  
-{{EquationsOfMotion6.gif}}\\+{{:EquationsOfMotion6.gif}}\\
  
  
 An advantage of this recursive formulation is that the approach is generalizable because there is substantially less bookkeeping required to keep track of the external forces and torques. An advantage of this recursive formulation is that the approach is generalizable because there is substantially less bookkeeping required to keep track of the external forces and torques.
 +
 +=== Sampling Rate ===
 +
 +Many people collect analog data at a higher rate than their motion capture data, which is the point rate. 
 +This is fine, as long as the higher rate is an integer multiple of the point rate. 
 +When force data are applied to a model, the resulting Link_Model_Based data are at point rate. 
 +This is because forces applied to segments cannot be calculated where the segment location is unknown (between point frames), 
 +i.e. there are no target data to generate segment locations for the ‘extra’ analog frames. 
 +However, the FORCE data retain the analog data rate. 
 +These ‘extra’ sample points are displayed as SUB frames within the point rate. 
 +The first subframe is synchronized with the point data, and it is this first subframe that is used for Inverse Dynamics calculations.
 +Other Link_Model_Based data, which are based on segments, are also sampled at the point rate, since segmental data can only ever be calculated at point rate.
  
 === Center of Mass of the Model === === Center of Mass of the Model ===
visual3d/documentation/kinematics_and_kinetics/inverse_dynamics.1721157954.txt.gz · Last modified: 2024/07/16 19:25 by sgranger