## Translating Goals into Action

a. Inverse Kinematics The smooth and simple hand trajectory described previously represents a kinematic plan. Before that plan can be formulated, the motor system must estimate both current hand position and the direction and magnitude of the movement needed to reach the target. Estimation of current hand position is based on two sources: Vision and proprioception. Muscle afferents from the arm provide the information necessary for estimating the orientation of each limb segment relative to its proximal joint. If the motor system has this information, it can compute the hand position with respect to the body. The computation of limb position from a proximal, joint-coordinate-based system to a distal, hand-centered coordinate system is called forward kinematics. If someone moves a blindfolded person's hand, he or she still has a pretty good idea of that hand's location. This ability depends primarily on the computation of forward kinematics from the length sensors in the muscles. If the motor system knows the length of the limb's muscles, it knows the angles of its joints and, through forward kinematics, can compute the location of the hand. The inverse of this computation maps hand position to the joint angles that are appropriate for it. In order to move the hand to a desired position, the motor system needs information about what joint angles the muscles need to achieve in order to move the limb segments to that position. This computation is termed inverse kinematics. In other words, if the motor system knows the desired hand position, it can compute the joint angles needed to put the hand in that position through the computation of inverse kinematics.

b. Inverse Dynamics In addition to computing the positions of the joints and the hand for a desired limb trajectory (kinematics), the motor system must estimate how much torque to produce on each joint (dynamics). Accordingly, the motor system must translate a desired motion of the end effector into a pattern of muscle activations. This does not imply that the brain calculates or represents the joint torques in absolute terms, joint by joint, but rather that the neural network must solve this problem to generate motor commands that will achieve the goal. Consider the torques needed to lift a full cup of coffee in contrast with those needed to lift an empty cup. Although the hand trajectories in the two cases may match perfectly, torques on the elbow will differ. Therefore, the motor system must take into account the weight of objects before it sends motor commands to the muscles. The computation that estimates the motion that will occur as a result of an applied force is called forward dynamics. The mass of objects held in the hand affects this computation: Activation of the biceps at a certain level will flex the elbow by a smaller amount for a full cup than for an empty cup. Forward dynamics consists of predicting the elbow angle after the biceps receives its activation command. The ability to predict the sensory consequences of motor commands relies on this computation. The inverse of this computation, called inverse dynamics, allows the motor system to transform the desired motion of the limb into the patterns of muscle activation that produce the torques required for the task.

However, in everyday life, even movements as simple as lifting a coffee cup can encounter impediments. When something disturbs arm movements (e.g., an unexpected change in the load on the hand), movements lose their smooth and regular character. However, provided that the perturbations have high predictability, with practice the movements again become straight in terms of hand trajectory. This convergence toward a straight, simple trajectory in hand coordinates (rather than joint coordinates) further supports the idea that the motor system plans movements in terms of the position of the hand and other end effectors rather than joint angles or patterns of muscle activity. In other words, the motor system plans in terms of goals rather than the components of movement. Motor learning and memory often under lies the ability to make smooth, straight movement despite external perturbations and the forces of each part of a limb acting on the others.

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