Planar two-segment limb model (equations of motion)

Builds the analytic dynamics of a planar two-link limb with distributed segment mass: the mass matrix M(q), the Coriolis/centrifugal matrix, the gravity vector, and forward/inverse dynamics. Angles are joint angles (proximal, then distal relative to the proximal segment), measured so gravity acts in -y.

Usage

planarLimbModel(
  mass,
  length,
  com = length/2,
  inertia = mass * length^2/12,
  g = 9.81
)

Arguments

mass

Length-2 segment masses (kg).

length

Length-2 segment lengths (m).

com

Length-2 distances of each segment centre of mass from its proximal joint (m); default length / 2.

inertia

Length-2 segment moments of inertia about the CoM (kg m^2); default the thin-rod mass * length^2 / 12.

g

Gravitational acceleration (m/s^2, default 9.81; use 0 for a horizontal-plane / no-gravity model).

Value

a planar_limb_model: functions M(q), coriolis(q, qd) (matrix), gravity(q), forward_accel(q, qd, tau), inverse_dynamics(q, qd, qdd), energy(q, qd) (kinetic, potential, total), and ndof = 2.

References

Spong MW, et al. (2006) Robot Modeling and Control.

See also

forwardDynamics(), predictiveSimulation()

Examples

m <- planarLimbModel(mass = c(7, 3), length = c(0.4, 0.4))
m$energy(c(0, 0), c(1, 0))$total
#> [1] 0.7466667