![]() ![]() #INVERSE DYNAMICS CALCULATOR TRIAL#Suppose that instead of selecting a direct path for the hand to follow on its way to a target, the motor system actually selects a convenient set of muscle torques and then, perhaps after some trial and error in the planning process, allows the hand to get to the target through a path that may be straight or may just as well be circuitous. Suppose the inverse dynamics problem is so hard for the motor system that it effectively sidesteps it. One reason that it is interesting to ask how the joint angles of the arm change during aiming movements is to learn how the motor system solves the inverse dynamics problem. The inverse dynamics problem is the one that usually must be solved in planning movements to spatial targets. ![]() The inverse dynamics problem is the problem of determining the torques that should be applied to the levers given that the endpoint of the levers is supposed to traverse some path. The muscle torques are selected on the basis of a chosen path for the hand to follow through extrapersonal space.ĭetermining how the endpoint of a system of hinged levers will be displaced when certain torques are applied to the levers is called the forward dynamics problem. Muscle torques are applied at these joints to cause the arm to move. Rosenbaum, in Human Motor Control, 1991 Hand-Space versus Joint-Space PlanningĪs the hand moves to pick up an object, the angles of the shoulder and elbow joints usually change. The time history of the actuator forces and torques for path 3 is also shown in the figure.ĭavid A. The unique performance of the four-legged mechanism is obvious in path 3. Point 4 is tangent to the singularity line and we observe a peak occurrence at the power consumption plot. As expected, the power consumption tends to infinity when the singularity line is passed, at points 2 and 3 in three-legged, and at points 5 and 6 in Gough–Stewart. Path 3 crosses the singularity line in both three-legged and Gough–Stewart, except four-legged, which enjoys a singular-free plane. It is notable that the mean value of power consumption for three-legged is still lower than that of Gough–Stewart, even though Gough–Stewart is not close to any singularities in path 2. This results in a jump in the power consumption plot, as shown in the figure. Path 2 has a higher amplitude than path 1, and in three-legged it approaches the singular area at point 1 in the figure. None of the mechanisms encounters any singular points in path 1. Power consumption for path 1 shows three-legged has a relatively lower mean power consumption compared to the four-legged, and significantly better than Gough–Stewart. The time history of the power consumption for the three mentioned paths is plotted in the figure. 30.8, for the center of the moving platform to follow. ![]() Next, we have defined three paths, as shown in Fig. ![]() However, three-legged and Gough–Stewart mechanisms encounter some singular points. 30.5, the four-legged mechanism has a singularity-free plane. We have plotted the nonsingular area for this orientation at z=0.1 m in the top plots in Fig. In all the simulations, the orientation of the moving platform is fixed at +20 for each of the three Euler angles. To analyze the singularity effects on dynamic responses of the mechanisms, we have solved the inverse dynamic problem for different paths. ![]()
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