Ngành này tập trung vào loài người, tuy một vài khía cạnh của động vật cũng thỉnh thoảng được nghiên cứu. Động vật ở đây có thể được nghiên cứu như là những chủ thể độc lập, hoặc – một cái nhìn gây tranh cãi hơn – được nghiên cứu như một cách tiếp cận đến sự hiểu biết bộ máy tâm thần của con người (qua tâm lý học so sánh). | 38 3 MATHEMATICAL AND FEATURE MODELS OF ASSEMBLIES Base Side View X Direction FIGURE 3-5. Schematic Diagram of Matrix Transforms Applied to the stapler. Left The parts of the stapler have been replaced by blobs. Right Straight-line arrows have been added to relate frames on the same part. Curved arrows have been added linking the coordinate frames of assembly features on different parts to indicate which ones are to be joined in order to assemble the parts. Double curved lines indicate the KCs that were identified in Chapter 1. FIGURE 3-6. Schematic Representation of a Transform. The transform T contains a translational part represented by vector p and a rotational part represented by matrix R. Vector p is expressed in the coordinates of frame 1. Matrix R rotates frame 1 into frame 2. basis transform T is Cl C2 C3 P Cl C2 C3 Pl Cl C2 C3 P3 0 0 0 1 3-2 where vector p is expressed in the coordinates of the original frame and r y are the direction cosines of axis i in frame 1 to axis j in frame 2. Transform T can be used to calculate the coordinates of a point in the second coordinate frame in terms of the first coordinate frame. The coordinates of a point are given by vectors are assumed to be column vectors so a transposed vector is a row vector. On a component-by-component X y z 3-3 . MATRIX TRANSFORMATIONS 39 Then in general if q is a vector in the second frame its coordinates in the first frame are given by q -. then 90 about y in the same frame. However w rot z 90 rot y 9Q u 3-10 q qt 1 ị Rq p 3-4 This says that q is obtained by rotating q by R and then adding p. Suppose a transform T consists only of matrix R and suppose that we want to find the coordinates of the end of a unit vector along the z axis of the rotated second frame in terms of the unrotated first frame. The calculation is 3-5 This result shows that the columns of matrix R tell where the coordinate axes have rotated. That is the first column tells where the X axis went and so on. The elements of
