We performed computer simulations for reaching movements of a two-link arm moving in the horizontal plane, as illustrated in Figure 2. The dynamics of a two-link arm is expressed by the following differential equation: Here, $\theta i$ and $\tau i$ are the angle and actuated torque of joint $i$. In addition, $mi,li,si$, and $Ii$ represent the mass, length, distance from the center of mass to the joint, and rotary inertia around the joint of link $i$, respectively; $bi$ represents the coefficient of viscosity of joint $i$. The values of these physical parameters are provided in Table 1.

$\tau 1=(I1+I2+2m2l1s2cos\theta 2+m2l12)\theta \xa81+(I2+m2l1s2cos\theta 2)\theta \xa82-m2l1s2(2\theta \u02d91+\theta \u02d92)\theta \u02d92sin\theta 2+b1\theta \u02d91,\tau 2=(I2+m2l1s2cos\theta 2)\theta \xa81+I2\theta \xa82+m2l1s2\theta \u02d912sin\theta 2+b2\theta \u02d92.$

(5.1)Table 1:

Parameters . | Link 1 . | Link 2 . |
---|---|---|

Mass: $mi$ (kg) | 1.680 | 1.644 |

Length: $li$ (m) | 0.325 | 0.367 |

COM: $si$ (m) | 0.1417 | 0.2503 |

Inertia: $Ii$ (kg$\xb7m2$) | 0.0522 | 0.1475 |

Viscosity: $bi$ (kg$\xb7m2$/s) | 0.2 | 0.2 |

Parameters . | Link 1 . | Link 2 . |
---|---|---|

Mass: $mi$ (kg) | 1.680 | 1.644 |

Length: $li$ (m) | 0.325 | 0.367 |

COM: $si$ (m) | 0.1417 | 0.2503 |

Inertia: $Ii$ (kg$\xb7m2$) | 0.0522 | 0.1475 |

Viscosity: $bi$ (kg$\xb7m2$/s) | 0.2 | 0.2 |

Figure 2:

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