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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 for Rotation

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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.
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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.
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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:

Kinematic Equations: Problem Solving

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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...

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Related Experiment Video

Updated: Jul 13, 2026

Estimation of Contact Regions Between Hands and Objects During Human Multi-Digit Grasping

Estimation of Contact Regions Between Hands and Objects During Human Multi-Digit Grasping

Published on: April 21, 2023

Finger kinematic modeling and real-time hand motion estimation.

P Cerveri¹, E De Momi, N Lopomo

¹Bioengineering Department, Politecnico di Milano University, Piazza Leonardo da Vinci 32, I-20133, Milan, Italy. pietro.cerveri@polimi.it

Annals of Biomedical Engineering

|August 19, 2007

Summary

This study presents a real-time finger motion tracking system using a multi-camera setup and a kinematic hand model. The validated system accurately reconstructs finger movements for biomechanical analysis.

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Area of Science:

Biomechanics
Motion Capture
Robotics

Background:

Accurate quantitative reconstruction of finger movements is crucial for biomechanical analysis and human-computer interaction.
Existing methods often face challenges in real-time performance and precision.

Purpose of the Study:

To develop and experimentally evaluate a real-time finger motion reconstruction system.
To validate a kinematic hand model for precise biomechanical analysis.

Main Methods:

Utilized a multi-camera system with 24 surface markers and a hierarchical kinematic hand model with 22 degrees of freedom.
Implemented automatic calibration based on anthropometric data and functional finger posture constraints.
Employed automatic marker labeling and a predictive filter for motion tracking.

Main Results:

Achieved high intra-subject repeatability for model calibration (0.5-2 mm).
Demonstrated satisfactory kinematic estimation accuracy (RMSE up to 3.25 mm) and motion reproducibility (R² up to 0.96).
Confirmed real-time capability with a processing/visualization frequency of 50 Hz and <1% marker occlusion during fast grasping.

Conclusions:

The developed system provides accurate and repeatable real-time finger motion reconstruction.
The validated kinematic hand model is effective for biomechanical analysis.
The system shows potential for applications requiring precise hand movement tracking.