{"id":582,"date":"2017-12-29T17:45:54","date_gmt":"2017-12-29T17:45:54","guid":{"rendered":"https:\/\/selfreconfigurable.com\/N3W\/?p=582"},"modified":"2018-01-02T23:09:29","modified_gmt":"2018-01-02T23:09:29","slug":"sensor-based-distance-determination-for-centers-of-two-cells-chained-through-a-third-cell","status":"publish","type":"post","link":"https:\/\/selfreconfigurable.com\/?p=582","title":{"rendered":"Sensor-Based Distance Determination for Centers of Two Cells Chained Through a Third Cell"},"content":{"rendered":"

SENSOR-BASED DISTANCE DETERMINATION FOR CENTERS OF TWO CELLS CHAINED THROUGH A THIRD CELL<\/h1>\n
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Certain lengths and angles can either be measured with sensors or are known constants that can be used to calculate the distance between the centers of two cells connected to a middle (third) cell such that they are chained in series. In order to determine the distance, each involved module within each cell would have to perform calculations on shared readings from both its own sensors and sensors on the other modules that are involved. In Figures 22a and 22b, 3 cells A, B, and C are drawn as three-dimensional green wire frames to represent the core of the cells (i.e., the cube-shaped region that doesn’t include the telescoping legs and connecting plates). The red numbered lines represent the measureable sections, they are either the distance from the center of the cell cube to the center of the face on the cube surface (all are equal and constant), or the length of the telescoping leg (each one is a variable value). There are two ways that 3 cells can be chained in series. One is shown in Figure 22a, where two cells (A & C) are connected to the middle cell (B) on opposite sides through it along the y-axis. In either case, the numbered red lines are:<\/p>\n

    \n
  1. Cell cube center to center of face for cell A connected to 2<\/li>\n
  2. Leg of cell A connected to 1 and 3<\/li>\n
  3. Leg of cell B connected to 4 and 2<\/li>\n
  4. Cell cube center to center of face for cell B connected to 3 and 5<\/li>\n
  5. Cell cube center to center of face for cell B connected to 4 and 6<\/li>\n
  6. Leg of cell B connected to 5 and 7<\/li>\n
  7. Leg of cell C connected to 6 and 8<\/li>\n
  8. Cell cube center to center of face for cell C connected to 7<\/li>\n<\/ol>\n

    The lengths of the “cell cube center to center of face” sections are all equal to each other in length\u00a0L\u00a0(i.e.,\u00a0L1\u00a0=\u00a0L4\u00a0=\u00a0L5\u00a0=\u00a0L8\u00a0=\u00a0L). For simplicity, all angle values written in formulas in this articleare limited to a single-cycle range of\u00a0angle\u00a0(0 \u2264\u00a0angle\u00a0< 2\u03c0).\"\"The other is shown in Figure 22b, where two cells (A & C) are connected to the middle cell (B) on adjacent sides through it along the positive y-axis, positive z-axis, and the x-y-z axes origin (where the 3 axes intersect).\"\"<\/p>\n

    In Figure 22c, the focus is on only some of the red lines, sections 1, 2, and 3 (or alternatively, sections 6, 7, and 8), in Figures 22a and 22b. Vector\u00a0r1\u00a0(line segment\u00a0OA) corresponds to sections 2 and 3 in Figures 22a and 22b, and vector\u00a0r2\u00a0(line segment\u00a0AC) corresponds to section 1 in Figures 22a and 22b. Points C1\u00a0and C2\u00a0are actually two possible graphical representations of a single point C, which is the center of the cell cube. The actual sensors are the universal joint horizontal and vertical angles, the connecting plate rotation angle, and the telescoping leg length. Readings from these sensors can be used as input values in conversion formulas as part of the process to perform the distance calculations. Since\u00a0\u03b8\u00a0corresponds to the pivot angle of the leg, and the leg pivots on the face of the cell cube, it is never going to be more than a magnitude of 90\u00b0 (i.e., 0 \u2264 |\u03b8| \u2264 \u03c0\/2).<\/p>\n

    \"\"<\/p>\n

    The following equations written in terms of\u00a0r\u00a0are 3-dimensional vector and magnitude formulas:<\/p>\n