Appendix:
Definitions of dimensions and angles on this site …(VC)
This section explains how dimensions and angles are defined in the diagrams used in each chapter.
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Dimensions
[1] About one-dimensional vector notation
A line segment, with one end marked by a dot and the other by an arrow, is treated as a one-dimensional vector with direction, and its details are defined as follows.
・ In the up and down directions, the scalar of an upward vector is a positive value, and the scalar of a downward vector is a negative value.
・In the left-right direction, the scalar of a vector pointing to the right is a positive value, and the scalar of a vector pointing to the left is a negative value.
・Multiplying the scalar quantity of each vector by -1 means swapping the start and end points of the vector and reversing its direction.
In this way, by representing the direction with a sign, a one-dimensional vector can be treated as a scalar quantity. If we let A be the scalar quantity of a certain vector, and define A(+) > 0 and A(−) < 0 depending on the direction, then the relationship between the scalar quantity and the vector can be summarized as follows.
In the horizontal direction:
In the vertical direction:
[2] Absolute dimensions without direction
A line segment with arrows at both ends is treated as an absolute dimension without direction. The scalar quantities of dimensions expressed using this notation are always positive and can represent lengths in any direction, including diagonal directions as well as vertical and horizontal directions.
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Angle notation
[1] Signed angles
The angle, indicated by a dot at one end and an arrow at the other, is treated as a quantity to distinguish the direction of rotation, and its details are defined as follows.
・The scalar value of an angular rotation in the counterclockwise direction is positive, and the scalar value of an angular rotation in the clockwise direction is negative.
・Multiplying the scalar quantity of each angle by -1 means swapping the start and end points of the angle and reversing its direction.
Let φ be a scalar quantity at a certain angle, and when φ(+)>0 and φ(-)<0, the relationship between the direction of the angle and the scalar quantity is as follows.
It should be noted that the sign of rotation varies depending on the convention, and therefore, the formulas and results derived based on this will depend on the definition adopted.
[2] Absolute angles without direction
Angles indicated by arrows at both ends are treated as absolute angles without direction. The scalar quantity of an angle expressed in this notation is always positive and is interpreted as a pure angle that does not distinguish the direction of rotation.
