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Kinematic Equations - II

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 - III

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 - I

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:

Relative Motion Analysis using Rotating Axes

Relative Motion Analysis using Rotating Axes

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it instrumental in...

Kinematic Equations: Problem Solving

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...

Kinematic Equations for Rotation

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...

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Related Experiment Video

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Capturing Dynamic Finger Gesturing with High-resolution Surface Electromyography and Computer Vision

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Tracking whole hand kinematics using extended Kalman filter.

Qiushi Fu¹, Marco Santello

¹School of Biological and Health Systems Engineering, Arizona State University, Tempe, AZ 85287 USA. qiushifu@asu.edu

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference

|November 25, 2010

Summary

This study presents a method for tracking whole hand movements using an extended Kalman filter (EKF) and active surface markers. The developed framework achieves 2-4 mm accuracy in hand tip positioning.

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Area of Science:

Biomechanics
Robotics
Computer Vision

Background:

Accurate tracking of whole hand kinematics is crucial for applications in human-computer interaction, prosthetics, and surgical robotics.
Existing methods often face challenges with computational complexity and marker occlusion.

Purpose of the Study:

To develop and validate a computationally efficient framework for tracking whole hand kinematics using active surface markers and an extended Kalman filter (EKF).
To assess the accuracy and feasibility of the proposed method for real-time motion capture.

Main Methods:

A 29-degree-of-freedom hand model was constructed, incorporating global posture, wrist, and digit articulations.
A marker protocol with 4 markers on the forearm and 20 on digit joints was employed.
The state space was divided into four subspaces, each estimated sequentially with an EKF to reduce computational load.

Main Results:

The framework demonstrated reasonably accurate results, with tip position errors ranging from 2 to 4 mm.
Performance was evaluated during tip-to-tip pinch tasks sampled at 120 Hz.

Conclusions:

The proposed EKF-based framework provides an efficient and accurate solution for tracking whole hand kinematics.
This method has potential applications in various fields requiring precise hand motion analysis.