"""Flanged timing pulley, 2GT (GT2), 3GT (GT3) and MXL. Axis along Z, the bottom flange's outer face on the XY plane; a flange of diameter F, 1 mm thick, at each end of the width W;
optionally the hub (diameter D, up to the overall length L) above the top flange. Set screws are not modelled.

detail = "full": the body at its outside diameter O.D. with its tooth grooves cut in. MXL grooves follow the published rack: depth 0.64, bottom 0.67, flanks 20 degrees (28 under 24 teeth).
2GT and 3GT publish the groove depth only, so the rounded groove's width is a proportion for looks, not for design. detail = "simple": a plain cylinder at O.D.
"""
import math

from steve import Model

profile = "2GT"  # Belt profile
teeth = 20  # Number of teeth
belt_width = 6  # mm Nominal belt width
bore = 5  # mm Bore
hub = False  # Hub above the top flange (shape B)
detail = "full"  # full: tooth grooves; simple: a plain cylinder at the outside diameter

# profile: {teeth: (P.D., O.D., D, F, E)}, D None: no hub offered. MISUMI FA Mechanical Components, High Torque Timing
# Pulleys 2GT pp. 1381-1382, 3GT pp. 1383-1384, Timing Pulleys MXL pp. 1389-1390 (2014), Number of Teeth / Dimension tables.
PULLEYS = {
    "2GT": {
        14: (8.91, 8.40, None, 13, 6), 15: (9.55, 9.04, None, 14, 7), 16: (10.19, 9.68, None, 14, 7), 18: (11.46, 10.95, None, 16, 8),
        20: (12.73, 12.22, None, 17, 9), 21: (13.37, 12.86, None, 18, 10), 22: (14.01, 13.50, 8, 18, 10), 24: (15.28, 14.77, 10, 20, 12),
        25: (15.92, 15.41, 10, 20, 12), 26: (16.55, 16.04, 10, 21, 12), 28: (17.83, 17.32, 10, 23, 14), 30: (19.10, 18.59, 11, 24, 15),
        32: (20.37, 19.86, 13, 25, 17), 34: (21.65, 21.14, 14, 27, 18), 36: (22.92, 22.41, 14, 27, 18), 38: (24.19, 23.68, 16, 29, 20),
        40: (25.46, 24.95, 17, 30, 21), 44: (28.01, 27.50, 19, 32, 23), 48: (30.56, 30.05, 22, 35, 26), 50: (31.83, 31.32, 22, 36, 27),
        60: (38.20, 37.69, 28, 42, 33),
    },
    "3GT": {
        16: (15.28, 14.52, None, 19, 11), 18: (17.19, 16.43, None, 21, 12), 20: (19.10, 18.34, None, 23, 14), 22: (21.01, 20.25, 12, 24, 16),
        24: (22.92, 22.16, 14, 26, 18), 25: (23.87, 23.11, 14, 27, 18), 26: (24.83, 24.07, 15, 28, 19), 28: (26.74, 25.98, 17, 30, 21),
        30: (28.65, 27.89, 19, 32, 23), 32: (30.56, 29.80, 20, 34, 25), 34: (32.47, 31.71, 22, 36, 27), 36: (34.38, 33.62, 24, 38, 29),
        40: (38.20, 37.44, 28, 42, 33), 44: (42.02, 41.26, 30, 46, 36), 48: (45.84, 45.08, 32, 49, 40), 50: (47.75, 46.99, 34, 51, 42),
        60: (57.30, 56.54, 36, 61, 52),
    },
    "MXL": {
        20: (12.94, 12.43, 9, 18, 11), 21: (13.58, 13.07, 9, 18, 11), 22: (14.23, 13.72, 9, 18, 11), 23: (14.88, 14.37, 11, 20, 13),
        24: (15.52, 15.02, 11, 20, 13), 25: (16.17, 15.66, 11, 20, 13), 26: (16.82, 16.31, 12, 22, 14), 27: (17.46, 16.96, 12, 22, 14),
        28: (18.11, 17.60, 12, 22, 14), 30: (19.40, 18.90, 14, 25, 16), 32: (20.70, 20.19, 14, 25, 16), 34: (21.99, 21.48, 14, 25, 16),
        36: (23.29, 22.78, 16, 28, 18), 38: (24.58, 24.07, 16, 28, 18), 40: (25.87, 25.36, 18, 30, 20), 42: (27.17, 26.66, 18, 30, 20),
        44: (28.46, 27.95, 20, 32, 23), 46: (29.75, 29.24, 20, 32, 23), 48: (31.05, 30.54, 22, 35, 25), 50: (32.34, 31.83, 22, 35, 25),
        60: (38.81, 38.30, 28, 44, 32), 72: (46.57, 46.06, 30, 52, 40),
    },
}
# profile: {nominal belt width: (A, W, L)}: Belt Nominal Width / Dimension tables of the same pages.
WIDTHS = {
    "2GT": {6: (7.0, 10.3, 18.0), 9: (10.0, 13.3, 21.0)},
    "3GT": {6: (7.3, 11.0, 19.0), 9: (10.3, 14.0, 22.0), 15: (16.3, 20.0, 28.0)},
    "MXL": {4.8: (6.0, 10.0, 16.5), 6.4: (7.5, 11.5, 18.0), 9.5: (11.0, 15.0, 22.0), 12.7: (14.0, 18.0, 25.0)},
}
FLANGE_THICKNESS = 1.0  # t1.0 on the same pages' drawings

if teeth not in PULLEYS[profile]:
    raise ValueError(f"{profile} tooth counts in the source: {', '.join(str(t) for t in PULLEYS[profile])}.")
if belt_width not in WIDTHS[profile]:
    raise ValueError(f"{profile} belt widths: {', '.join(str(w) for w in WIDTHS[profile])} mm.")
pd, od, d_hub, f, e = PULLEYS[profile][teeth]
a, w, l = WIDTHS[profile][belt_width]
if hub and d_hub is None:
    raise ValueError(f"{profile} {teeth} teeth: the source offers no hub for this size.")
if bore + 2 > e:
    raise ValueError(f"Bore {bore} leaves no wall under the teeth: at most {e - 2} mm.")

# profile: groove depth, from the Standard Tooth Profile drawings of the same pages (2GT 0.75; 3GT 1.14; MXL 0.64).
GROOVE_DEPTH = {"2GT": 0.75, "3GT": 1.14, "MXL": 0.64}
PITCH = {"2GT": 2.0, "3GT": 3.0, "MXL": 2.032}
GROOVE_WIDTH = 0.62  # x pitch: mouth of the rounded 2GT and 3GT grooves, a proportion for looks
MXL_BOTTOM = 0.67  # bottom of the MXL groove, same pages

if teeth not in PULLEYS[profile]:
    raise ValueError(f"{profile} tooth counts in the source: {', '.join(str(t) for t in PULLEYS[profile])}.")
if belt_width not in WIDTHS[profile]:
    raise ValueError(f"{profile} belt widths: {', '.join(str(w) for w in WIDTHS[profile])} mm.")
pd, od, d_hub, f, e = PULLEYS[profile][teeth]
a, w, l = WIDTHS[profile][belt_width]
if hub and d_hub is None:
    raise ValueError(f"{profile} {teeth} teeth: the source offers no hub for this size.")
if bore + 2 > e:
    raise ValueError(f"Bore {bore} leaves no wall under the teeth: at most {e - 2} mm.")

model = Model()
radius = od / 2
depth = GROOVE_DEPTH[profile]
if detail == "simple":
    with model.sketch("body_sketch", on="XY", name="Toothed body") as sk:
        sk.circle("body_od", (0, 0), radius)
else:
    if profile == "MXL":
        flank = math.tan(math.radians(28 if teeth < 24 else 20))
        half_bottom = MXL_BOTTOM / 2
        groove = [(half_bottom + depth * flank, 0.0), (half_bottom, depth), (-half_bottom, depth), (-half_bottom - depth * flank, 0.0)]
    else:
        half_mouth = GROOVE_WIDTH * PITCH[profile] / 2
        groove = [(half_mouth * math.cos(math.pi * i / 6), depth * math.sin(math.pi * i / 6)) for i in range(7)]
    outline = []
    for n in range(teeth):
        centre = 2 * math.pi * n / teeth
        for u, v in groove:
            angle = centre - u / radius
            outline.append(((radius - v) * math.sin(angle), (radius - v) * math.cos(angle)))
    with model.sketch("body_sketch", on="XY", name="Toothed body") as sk:
        sk.polyline("body_outline", outline, closed=True)
model.extrude("body", "body_sketch", distance=w, name="Toothed body")
with model.sketch("flange_low_sketch", on="XY", name="Lower flange") as sk:
    sk.circle("flange_low_od", (0, 0), f / 2)
model.extrude("flange_low", "flange_low_sketch", distance=FLANGE_THICKNESS, name="Lower flange")
model.plane("flange_plane", on="XY", offset=w - FLANGE_THICKNESS, name="Upper flange face")
with model.sketch("flange_high_sketch", on="flange_plane", name="Upper flange") as sk:
    sk.circle("flange_high_od", (0, 0), f / 2)
model.extrude("flange_high", "flange_high_sketch", distance=FLANGE_THICKNESS, name="Upper flange")
top = w
if hub:
    model.plane("hub_plane", on="XY", offset=w, name="Hub base")
    with model.sketch("hub_sketch", on="hub_plane", name="Hub") as sk:
        sk.circle("hub_od", (0, 0), d_hub / 2)
    model.extrude("hub_body", "hub_sketch", distance=l - w, name="Hub")
    top = l
with model.sketch("bore_sketch", on="XY", name="Bore") as sk:
    sk.circle("bore_d", (0, 0), bore / 2)
model.extrude("bore_cut", "bore_sketch", distance=top, op="cut", name="Bore")
model.material("aluminum-generic", color="#c9ccd0")
result = model.result()