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:
$τ1=(I1+I2+2m2l1s2cosθ2+m2l12)θ¨1+(I2+m2l1s2cosθ2)θ¨2-m2l1s2(2θ˙1+θ˙2)θ˙2sinθ2+b1θ˙1,τ2=(I2+m2l1s2cosθ2)θ¨1+I2θ¨2+m2l1s2θ˙12sinθ2+b2θ˙2.$
(5.1)
Here, $θi$ and $τi$ 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.
Table 1:
Physical Parameters of a Two-Link Arm.
Mass: $mi$ (kg) 1.680 1.644
Length: $li$ (m) 0.325 0.367
COM: $si$ (m) 0.1417 0.2503
Inertia: $Ii$ (kg$·m2$0.0522 0.1475
Viscosity: $bi$ (kg$·m2$/s) 0.2 0.2
Mass: $mi$ (kg) 1.680 1.644
Length: $li$ (m) 0.325 0.367
COM: $si$ (m) 0.1417 0.2503
Inertia: $Ii$ (kg$·m2$0.0522 0.1475
Viscosity: $bi$ (kg$·m2$/s) 0.2 0.2
Figure 2:

A two-link arm moving in the horizontal plane (X-Y plane).

Figure 2:

A two-link arm moving in the horizontal plane (X-Y plane).

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