Lecture 3

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Figure 2.1 when the crank is set to 120, the angels of the coupler link and the

rocker arm are also known.

However, it is not true for multiple degree of freedom mechanism, like robots

Robots

Open loop mechanisms.

each joint variable must be known in order to know where the hand of the

robot is.

Due to deflection , hand actual position is difficult to find as shown in figure 2.2

So, it is important to continuously monitor all joint/end point.

Lecture 3

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Lecture 3

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Lecture 3

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Point has only 3 DOF, and oly move along the three reference axes.

Rigid body has 6 DOF (move along X, Y, and Z, but also rotate about three axis)

6 pieces of information

However, equation 2.9 shows 12 pieces of information (9 for orientation and 3 for

position).

Means, we need 6 constraints equations to reduce the amount of information from

12 to 6 pieces.

Lecture 3

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(do it yourself)

Lecture 3

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Pure Translation

If a frame (which may also be representing an object) moves in space without

any change in its orientation.

The directional unit vectors remain in the same direction and thus do not

change.

All that changes is the location of the origin of the frame relative to the

reference frame as shown in figure.

The new location of the frame relative to the reference frame can be found

using:

The first three columns represent no rotational movement, while the last

column represents the translation.

Lecture 3

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Please note that the directional vectors remain the same after a pure

translation.

Homogeneous transformation matrices facilitate the multiplication of matrices,

resulting the same dimensions as before.