A trigonometric saw-cut centering jig assembly disposed for use upon the saw table of a powered table saw comprising a saw blade disposed along a cutting plane and a longitudinal translation channel disposed parallel the cutting plane, the jig assembly comprising
- a moveable component;
- a fixed component;
- and
- a displacement accommodating component;
- the moveable component overlying the fixed component, the position of the moveable component set by clamp means to the fixed component;
- the moveable component comprising
- a plate comprising an upper surface and an underside;
- a moveable curb attached to the moveable component's plate;
- a guide fence disposed parallel the saw blade's cutting plane such that a workable piece to be cut positioned snugly against the guide fence and in alignment with the saw blade may be advanced along the saw blade's cutting plane longitudinally in a direction away from the operator and cut by operation thereof;
- the moveable component configured with a running abutment edge disposed at an angle from the saw blade's cutting plane;
- the moveable component, when released from its clamp means to the fixed component, manually moveable by advancement longitudinally in a direction away from the operator and withdrawal longitudinally in a direction toward the operator parallel the saw blade's cutting plane, a distance of longitudinal advancement or withdrawal defined herein as a longitudinal displacement adjusting factor;
- the fixed component overlying the displacement accommodating component, interconnected to it by clamp means, and comprising
- a plate comprising an upper surface and an underside;
- and
- a fixed curb attached to the fixed component's plate and disposed in the manner of a stop wherein as the moveable component is advanced along the saw blade's cutting plane longitudinally in a direction away from the operator, a portion of the moveable curb is brought into abutment with a portion of the fixed curb;
- the fixed component configured with an angled abutment ridge disposed at the same angle from the saw blade's cutting plane as that of the moveable component's running edge;
- the displacement accommodating component comprising
- a plate comprising an upper surface and an underside;
- and
- a longitudinal translation rail mated to and interconnected with the saw table's longitudinal translation channel such that the displacement accommodating component may be repositioned upon the saw table parallel the saw blade's cutting plane and set by clamp means therefor;
- the moveable component disposed by positioning it with its running abutment edge in contact with the fixed component's angled abutment ridge such that upon advancing the moveable component along the saw blade's cutting plane longitudinally in a direction away from the operator or withdrawing it along the saw blade's cutting plane longitudinally in a direction toward the operator, in a direction parallel the cutting plane of the saw blade, to position the moveable component for the saw's cutting operation, the advancement or withdrawal conforms only to a path provided by the angular disposition of the moveable component's running abutment edge and the disposition of the fixed component's angled abutment ridge with which it remains in contact during the moveable component's advancement or withdrawal, the angle so provided defining a jig assembly's angle determinant means, wherein the angle so determined comprises one of a triangle in which the moveable component's running abutment edge and the fixed component's angled abutment ridge with which it remains in contact comprises a triangle's side disposed angularly away from the saw blade and represents the hypotenuse of the triangle, the longitudinal distance of advancement or withdrawal in a direction parallel the plane of the saw blade represents the adjacent side of the triangle and the distance of lateral displacement from the saw blade represents the opposite side of the triangle;
- and wherein further, the trigonometric sine of the angle so determined is equal to the opposite side of the triangle divided by the hypotenuse and the trigonometric cosine of the angle so determined is equal to the adjacent side of the triangle divided by the hypotenuse;
- such that as the moveable component is moved, respectively, toward or away from the operator, the guide fence is moved, respectively, toward or displaced from the saw blade effecting a separation distance therefrom, transverse the saw blade's cutting plane, the separation distance herein defined as the lateral displacement adjusting factor;
- the movements represented by angular vectors wherein the distance of the moveable component's advancement or withdrawal is represented by a longitudinally disposed vector comprising a first side of a right triangle;
- and the transverse separation distance between the moveable component's fence and the saw blade is represented by a laterally disposed vector comprising a second side of the triangle, the interior angle between the first and second sides comprising a right angle;
- and a projection of the angle determinant means intersecting the first and second sides comprising a third side of a represented right triangle representing the hypotenuse thereof;
- the first side thereof representing a cosine related side and the second side thereof representing a sine related side;
- the vertex of the angle measured between the angle determinant means and the plane of the saw blade comprising the most longitudinally distal portion of the right triangle;
- wherein further, upon advancing the moveable curb such that it is brought together in abutment with the fixed curb, providing a longitudinal displacement adjusting factor of zero, the moveable component may be laterally repositioned with reference to the displacement accommodating component such that the guide fence is caused to abut the saw blade, providing a lateral displacement adjusting factor of zero;
- whereupon a workable piece may be positioned with its width disposed snugly between the curbs, providing a longitudinal displacement adjusting factor equal to the distance between the curbs, thereby laterally displacing the guide fence from the saw blade a distance comprising by reason of the angle measured between the angle determinant means and the plane of the saw blade and the sine and cosine values for that angle, a lateral displacement adjusting factor comprising the product of the longitudinal displacement adjusting factor and a fraction equal to the ratio of the sine value for the angle measured between the angle determinant means and the plane of the saw blade to the cosine value therefor, wherein the workable piece may be positioned such that a corresponding fraction of its width is disposed between the guide fence and the saw blade.