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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.
ParametersLink 1Link 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·m20.0522 0.1475 
Viscosity: bi (kg·m2/s) 0.2 0.2 
ParametersLink 1Link 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·m20.0522 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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