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Related Concept Videos

Kinematic Equations: Problem Solving01:15

Kinematic Equations: Problem Solving

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...
Orthogonal Trajectories01:26

Orthogonal Trajectories

Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
Kinematic Equations - II01:17

Kinematic Equations - II

The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
Kinematic Equations - III01:18

Kinematic Equations - III

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...
Kinematic Equations for Rotation01:30

Kinematic Equations for Rotation

In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...
Kinematic Equations - I01:26

Kinematic Equations - I

When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of motions are derived for such cases where the acceleration of the object is constant. The first kinematic equation gives an insight into the relationship between velocity, acceleration, and time. We can see, for example:

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Related Experiment Video

Updated: Jul 10, 2026

Sit-to-stand-and-walk from 120% Knee Height: A Novel Approach to Assess Dynamic Postural Control Independent of Lead-limb
08:24

Sit-to-stand-and-walk from 120% Knee Height: A Novel Approach to Assess Dynamic Postural Control Independent of Lead-limb

Published on: August 30, 2016

Can a kinetic optimization criterion predict both arm trajectory and final arm posture?

Yasuhiro Wada1, Kazuhiro Yamanaka, Yousuke Soga

  • 1Department of Electrical Engineering, Nagaoka University of Technology, Nagaoka-shi, Japan. ywada@nagaokaut.ac.jp

Conference Proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference
|October 20, 2007
PubMed
Summary

Human arm movements in 3D space are best predicted by the minimum commanded torque change model. This model accurately describes both hand trajectories and arm postures, advancing understanding of motor control.

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An Objective and Child-friendly Assessment of Arm Function by Using a 3-D Sensor

Published on: February 12, 2018

Area of Science:

  • Biomechanics
  • Robotics
  • Motor Control

Background:

  • Human arm movements on a plane exhibit straight, slightly curved paths and single-peaked bell-shaped velocity profiles.
  • Existing models, including minimum hand jerk and minimum torque change, explain 2D movements but lack 3D validation.

Purpose of the Study:

  • To quantitatively evaluate four optimal principle-based trajectory planning criteria in three-dimensional (3D) space for human arm movements.
  • To compare model predictions with measured 3D arm trajectories and postures.

Main Methods:

  • Analysis of four criteria: minimum hand jerk, minimum angle jerk, minimum torque change, and minimum commanded torque change.
  • Quantitative comparison of predicted 3D arm trajectories and postures against measured data.

Main Results:

  • The minimum commanded torque change criterion demonstrated the closest correspondence to measured human arm trajectories in 3D space.
  • This criterion also accurately predicted observed arm postures in three-dimensional movement.

Conclusions:

  • The minimum commanded torque change model provides the most accurate prediction for 3D human arm movement trajectories and postures.
  • This finding advances the understanding of motor planning and control in complex, three-dimensional workspaces.