Compute 3D lower-limb joint moments with inverse dynamics

Computes ankle, knee, and hip net moment vectors in 3D from joint-center coordinates, GRF, COP, and segment inertial properties, using a recursive link-segment Newton-Euler chain (foot -> shank -> thigh).

Usage

inverseDynamics3D(
  joints,
  grf,
  sampling_rate,
  angles = NULL,
  angular_velocity = NULL,
  angular_acceleration = NULL,
  inertial = NULL,
  angle_unit = c("radian", "degree"),
  model = c("newton_euler", "quasi_static"),
  body_mass = NULL,
  body_height = NULL,
  gravity = .GRAVITY,
  vertical = c("y", "z")
)

Arguments

joints: Matrix/data.frame with columns ankle_x, ankle_y, ankle_z, knee_x, knee_y, knee_z, hip_x, hip_y, hip_z, and - for model = "newton_euler" - the foot distal end toe_x, toe_y, toe_z.
grf: Matrix/data.frame with columns fx, fy, fz and optional cop_x, cop_y, cop_z (and, for model = "newton_euler", optional free moments tx, ty, tz).
sampling_rate: Sampling rate in Hz.
angles: Optional matrix/data.frame containing 3D joint angles with columns ankle_x, ankle_y, ankle_z, knee_x, knee_y, knee_z, hip_x, hip_y, hip_z.
angular_velocity: Optional 3D joint angular velocity table.
angular_acceleration: Optional 3D joint angular acceleration table.
inertial: Optional data.frame from estimateSegmentInertia(). Required for model = "newton_euler" unless body_mass is given; under model = "quasi_static" it only supplies an I * alpha correction and is ignored when omitted.
angle_unit: Unit of angle-related inputs: "radian" or "degree".
model: Which dynamics model to use: "newton_euler" (the default, the full recursive chain via inverseDynamicsRNE()) or "quasi_static" (the legacy massless-segment approximation; see inverseDynamics2D()).
body_mass: Body mass in kg, used to build the segment inertia table with estimateSegmentInertia() when inertial is not supplied.
body_height: Body height in m, used when segment lengths must be estimated from stature rather than measured from the markers.
gravity: Gravitational acceleration in m/s^2.
vertical: Which coordinate axis points up, "y" (default) or "z". Gravity acts along the negative of this axis, so it must match the laboratory convention of joints. The default follows this package's marker convention (x antero-posterior, y vertical, z medio-lateral) and the sagittal inverseDynamics2D(); note that force-plate hardware normally reports the vertical force as fz, so grf may need reordering to match. A mismatch is checked against the marker geometry and warned about, because the wrong axis silently removes every gravitational moment. Used only by model = "newton_euler"; the quasi-static model has no gravity term and therefore ignores it.

Value

A data.frame with time and moment components: *_moment_x, *_moment_y, *_moment_z. If angular velocity is available, *_power_total columns are included. model = "newton_euler" also returns the proximal joint reaction force components (ankle_fx, ankle_fy, ankle_fz, ...).

Details

See inverseDynamics2D() for what the two models compute and why the quasi-static one is retained only for reproducibility. The 3D moment balance uses an axisymmetric segment inertia and neglects the gyroscopic \(\omega \times I \omega\) term and any spin about the segment long axis, which is not observable from two joint centres.

References

Winter DA (2009). "Biomechanics and Motor Control of Human Movement." 4th ed. John Wiley & Sons.

Examples

n <- 200
joints <- data.frame(
  ankle_x = rep(0.00, n), ankle_y = rep(0.05, n), ankle_z = rep(0.00, n),
  toe_x   = rep(0.15, n), toe_y   = rep(0.01, n), toe_z   = rep(0.00, n),
  knee_x = rep(0.00, n),  knee_y = rep(0.45, n),  knee_z = rep(0.00, n),
  hip_x = rep(0.00, n),   hip_y = rep(0.85, n),   hip_z = rep(0.00, n)
)
grf <- data.frame(
  fx = rep(50, n), fy = rep(700, n), fz = rep(0, n),
  cop_x = rep(0.02, n), cop_y = rep(0, n), cop_z = rep(0, n)
)
out <- inverseDynamics3D(joints, grf, sampling_rate = 100, body_mass = 70)