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Sponsored by National Science Foundation  
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Dynamics is considered to be one of the most difficult and non-intuitive courses that engineering students encounter during their undergraduate study because the course combined basic Newtonian physics and various mathematical concepts such as vector algebra, geometry, trigonometry, and calculus and these were applied to dynamical systems.

Dynamics is an important engineering course for three reasons. First, it is essential to have a strong grasp of the concepts covered in the course when pursuing a degree in engineering. Second, it is a required course for many engineering departments and is the first engineering course that covers both difficult and abstract concepts. Third, for many capable students this course can become a roadblock to a career in engineering.

Haptic interfaces offer greater opportunity to present abstract concepts dynamically to the sense of touch combined with visual feedback in the Virtual Environment. Generally, haptic interface devices serve as special purpose hardware for information input and output with computers. Our sense of touch is an active, informative and useful perceptual system and it is the only human sense that enables us to modify and manipulate the world around us. It was suggested that something touched is more real than something seen

Figure 1. Touch virtual objects with haptic interface

The function of this project is to integrate haptic-augmented Virtual Environment technology into the course of ‘Dynamics’ for the undergraduate engineering students at Lamar University.

We identified the following exemplary Dynamics problems as shown in Table 1.

Table 1 Concepts and Exemplary Problems





Sliding and Rolling Motion

Motion of a block and a wheel on a plane


Impulse and Impact

An impact between a bowling ball and a bowling pin, or between two balls


Centrifugal and Centripetal Forces

A merry-go-round ride, or Particle waltz


Coriolis Acceleration

A slider on a rotating arm


Kinetics of Rigid Bodies

A piston-crank mechanism of an internal combustion engine

Problem 1Sliding and Rolling Motion
There are two cases. The two cases look similar but work differently for the block and the ball. One can feel the friction force with a haptic device.

  1. A block moving with an initial speed on the surface from left to right: because of the friction on the surface, the block gradually slows down, until it comes to a full stop. The block slides on the surface all the time.

Figure 2  A Sliding Block on a Flat Plane

  1. A ball (sphere) with an initial speed on the surface from left to right: because of the friction on the surface, the kinetic energy of linear motion is gradually converted into the kinetic energy of the rotational motion. This means that at the beginning of the motion, the ball is both sliding and rolling. At a certain moment, the ball is no longer sliding as the contact point between the ball and the surface has a zero velocity, which means there is no friction at the contact point. Thus the ball will keep moving at a constant speed. And this motion is pure rolling, without sliding.

Figure 3  A Rolling and Sliding Ball on a Flat Plane

Problem 2Impulse and Impact
There are two demos for this problem. By manipulating the ball with a haptic device, one can try different impact results.

  1. Two (billiard) balls collide with each other: direct impact or oblique impact. By pressing and holding the blue button of the haptic probe, one can drag one ball and try to hit the other

Figure 4  Two Balls in Collision

  1. One (bowling) ball hits a (bowling) pin. By pressing and holding the blue button of the haptic probe, one can drag the ball and try to hit the bowling pin.

Figure 5  Rolling ball and the Bowling Pin

Problem 3Centrifugal and centripetal forces
This demo shows particle-waltz example. Two particles are used to represent two persons. They are dancing like in a waltz. One particle is leading the other. The other particle follows the motion of the first particle, as if the two are connected with a rubber band. The force arrow shows the magnitude and the direction of the centripetal force. One can feel the centripetal force when dragging the ball with a haptic device.

Figure 6  Particle Waltz Example

Problem 4Coriolis acceleration and force
This demo shows Coriolis acceleration and its corresponding Coriolis force. It shows a rotating bar, which rotates at a constant speed. On the rotating bar, a slider block is moving at sine wave motion (autonomously). With a haptic device, one can feel the Coriolis force when following the motion of the slider.

Figure 7  Coriolis Force and Acceleration Example

Problem 5Kinetics of Rigid Body

 This demo shows the slider-crank mechanism of an internal combustion engine. Generally speaking, there are three types of planar motion: 1) linear translation; 2) rotation; 3) combined translation and rotation in a plane. In a slider-crank mechanism, the slider is moving at linear translational motion; the link BC is at rotational motion; the link AB is at combined translational and rotational motion. In this case, the slider is actually the piston of a car engine and it drives the crank and wheel (not drawn in this figure). One can drag the slider to move the mechanism with a haptic device.   

Figure 8  Slider-crank Mechanism Simulation


(c) Lamar University  

Acknowledgment: Partial support for this work was provided by the National Science Foundation's Course, Curriculum, and Laboratory Improvement (CCLI) program under Award No. 0737173 to Drs. W. Zhu, K. Aung, J. Zhou and M. Srinivasan. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.