{
  "$schema": "https://slfy.solidify.studio/schema/slfy-0.1.schema.json",
  "format": "slfy",
  "version": "0.1",
  "model": {
    "id": "quick-return-mechanism",
    "title": "Crank & Slotted-Lever Quick-Return Mechanism",
    "summary": "Whitworth crank and slotted-lever drive for a metal shaper. Constant-speed rotation of the bull gear drives a sliding block within the slotted rocker, producing a slow forward cutting stroke and a rapid return stroke.",
    "units": "mm",
    "parameters": [
      {
        "id": "r",
        "label": "Crank Radius",
        "symbol": "r",
        "value": 0.065,
        "min": 0.04,
        "max": 0.095,
        "step": 0.005,
        "unit": "m"
      },
      {
        "id": "c",
        "label": "Pivot Centre Distance",
        "symbol": "c",
        "value": 0.17,
        "min": 0.13,
        "max": 0.22,
        "step": 0.005,
        "unit": "m"
      },
      {
        "id": "L_lever",
        "label": "Rocker Arm Length",
        "symbol": "L",
        "value": 0.36,
        "min": 0.28,
        "max": 0.44,
        "step": 0.01,
        "unit": "m"
      },
      {
        "id": "L_link",
        "label": "Drag Link Length",
        "symbol": "l_d",
        "value": 0.11,
        "min": 0.08,
        "max": 0.16,
        "step": 0.005,
        "unit": "m"
      },
      {
        "id": "speed",
        "label": "Bull Gear Speed",
        "symbol": "n",
        "value": 30,
        "min": 10,
        "max": 60,
        "step": 5,
        "unit": "rpm"
      },
      {
        "id": "F_cut",
        "label": "Cutting Resistance",
        "symbol": "F_c",
        "value": 1500,
        "min": 500,
        "max": 3500,
        "step": 100,
        "unit": "N"
      }
    ],
    "parts": [
      {
        "id": "frame",
        "name": "Shaper Column & Guideway",
        "material": "castIron",
        "role": "housing",
        "position": [
          0,
          0,
          0
        ],
        "explode": [
          -0.14,
          0,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Heavy cast-iron column of the shaping machine",
          "role": "Anchors the bull gear spindle bearing, supports the lower rocker pivot pin, and provides top horizontal dovetail guideways for the reciprocating ram."
        },
        "shapes": [
          {
            "kind": "box",
            "position": [
              -0.08,
              0,
              -0.15
            ],
            "sx": 0.32,
            "sy": 0.52,
            "sz": 0.22
          },
          {
            "kind": "box",
            "position": [
              -0.04,
              -0.24,
              -0.06
            ],
            "sx": 0.44,
            "sy": 0.05,
            "sz": 0.38
          },
          {
            "kind": "box",
            "position": [
              0.04,
              0.22,
              -0.04
            ],
            "sx": 0.46,
            "sy": 0.06,
            "sz": 0.18
          },
          {
            "kind": "cylinder",
            "position": [
              0.06,
              0,
              -0.04
            ],
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.052,
            "h": 0.08
          },
          {
            "kind": "cylinder",
            "position": [
              0.06,
              "-c",
              0.01
            ],
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.034,
            "h": 0.07
          }
        ]
      },
      {
        "id": "bull_gear",
        "name": "Bull Gear Crank Disc",
        "material": "steel",
        "role": "moving",
        "explode": [
          0,
          0,
          0.12
        ],
        "cut": false,
        "info": {
          "summary": "Precision spur bull gear with radial crank pin guide",
          "role": "Rotates at uniform speed to orbit the adjustable crank pin, driving the sliding block back and forth inside the rocker arm."
        },
        "motion": {
          "kind": "rotate",
          "axis": "z",
          "speed": "speed / 60"
        },
        "mount": {
          "kind": "against",
          "target": "frame",
          "face": "+z",
          "shift": [
            0.06,
            0,
            0.01
          ]
        },
        "shapes": [
          {
            "kind": "gear",
            "rotation": [
              1.5708,
              0,
              0
            ],
            "rInner": 0.024,
            "h": 0.026,
            "teeth": 38,
            "module": 0.0055
          },
          {
            "kind": "cylinder",
            "position": [
              0,
              0,
              0.015
            ],
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.085,
            "h": 0.008
          },
          {
            "kind": "cylinder",
            "position": [
              0,
              "r",
              0.024
            ],
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.014,
            "h": 0.032
          }
        ]
      },
      {
        "id": "sliding_block",
        "name": "Crank Slide Die Block",
        "material": "bronze",
        "role": "moving",
        "explode": [
          0,
          0,
          0.14
        ],
        "cut": false,
        "info": {
          "summary": "Phosphor-bronze crank sliding block",
          "role": "Rotates freely on the bull gear crank pin while sliding within the rocker arm slot to convert uniform rotation into quick-return oscillation."
        },
        "mount": {
          "kind": "coaxial",
          "target": "bull_gear",
          "shift": [
            0,
            "r",
            0.024
          ]
        },
        "shapes": [
          {
            "kind": "box",
            "sx": 0.044,
            "sy": 0.042,
            "sz": 0.024
          },
          {
            "kind": "tube",
            "rotation": [
              1.5708,
              0,
              0
            ],
            "rOuter": 0.02,
            "rInner": 0.014,
            "h": 0.026
          }
        ]
      },
      {
        "id": "slotted_lever",
        "name": "Slotted Rocker Lever",
        "material": "forged",
        "role": "moving",
        "explode": [
          0,
          0,
          0.16
        ],
        "cut": false,
        "info": {
          "summary": "Long oscillating slotted arm pivoted at base",
          "role": "Driven by the crank slide block through an angle 2φ, producing a slow cutting stroke and rapid non-cutting return."
        },
        "motion": {
          "kind": "oscillate",
          "axis": "z",
          "speed": "speed / 60",
          "amplitude": "asin(r / c) * 180 / pi"
        },
        "mount": {
          "kind": "against",
          "target": "frame",
          "face": "+z",
          "shift": [
            0.06,
            "-c",
            0.038
          ]
        },
        "shapes": [
          {
            "kind": "cylinder",
            "position": [
              0,
              0,
              0
            ],
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.028,
            "h": 0.032
          },
          {
            "kind": "cylinder",
            "position": [
              0,
              0,
              -0.02
            ],
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.016,
            "h": 0.04
          },
          {
            "kind": "box",
            "position": [
              0,
              "L_lever / 2",
              0
            ],
            "sx": 0.054,
            "sy": "L_lever",
            "sz": 0.026
          },
          {
            "kind": "box",
            "op": "subtract",
            "position": [
              0,
              "c",
              0
            ],
            "sx": 0.044,
            "sy": "2 * r + 0.06",
            "sz": 0.03
          },
          {
            "kind": "cylinder",
            "position": [
              0,
              "L_lever",
              0
            ],
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.022,
            "h": 0.03
          },
          {
            "kind": "cylinder",
            "position": [
              0,
              "L_lever",
              0.01
            ],
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.012,
            "h": 0.046
          }
        ]
      },
      {
        "id": "connecting_link",
        "name": "Drag Link",
        "material": "steel",
        "role": "moving",
        "explode": [
          0,
          0.08,
          0.08
        ],
        "cut": false,
        "info": {
          "summary": "Short connecting link between rocker top and ram",
          "role": "Accommodates the slight vertical arc of the rocker arm tip while transmitting horizontal cutting force directly into the ram."
        },
        "motion": {
          "kind": "oscillate",
          "axis": "x",
          "speed": "speed / 60",
          "amplitude": "stroke / 2"
        },
        "mount": {
          "kind": "coaxial",
          "target": "slotted_lever",
          "shift": [
            "L_link / 2",
            "L_lever",
            0.026
          ]
        },
        "shapes": [
          {
            "kind": "box",
            "sx": "L_link",
            "sy": 0.024,
            "sz": 0.018
          },
          {
            "kind": "cylinder",
            "position": [
              "-L_link / 2",
              0,
              0
            ],
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.018,
            "h": 0.022
          },
          {
            "kind": "cylinder",
            "position": [
              "L_link / 2",
              0,
              0
            ],
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.018,
            "h": 0.022
          }
        ]
      },
      {
        "id": "ram",
        "name": "Shaper Ram",
        "material": "castIron",
        "role": "moving",
        "explode": [
          0,
          0.12,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Rigid reciprocating ram sliding on top guideways",
          "role": "Translates horizontally to carry the tool head across the workpiece and absorb high cutting thrust."
        },
        "motion": {
          "kind": "oscillate",
          "axis": "x",
          "speed": "speed / 60",
          "amplitude": "stroke / 2"
        },
        "mount": {
          "kind": "against",
          "target": "frame",
          "face": "+y",
          "shift": [
            0.08,
            0.026,
            0.01
          ]
        },
        "shapes": [
          {
            "kind": "box",
            "position": [
              0,
              0,
              0
            ],
            "sx": 0.48,
            "sy": 0.065,
            "sz": 0.14
          },
          {
            "kind": "box",
            "position": [
              0,
              -0.038,
              0
            ],
            "sx": 0.48,
            "sy": 0.018,
            "sz": 0.11
          },
          {
            "kind": "box",
            "position": [
              "-0.12 + L_link / 2",
              -0.04,
              0.05
            ],
            "sx": 0.036,
            "sy": 0.046,
            "sz": 0.034
          },
          {
            "kind": "cylinder",
            "position": [
              0,
              0.048,
              0
            ],
            "r": 0.016,
            "h": 0.044
          }
        ]
      },
      {
        "id": "tool_head",
        "name": "Tool Head & Clapper Box",
        "material": "steelDark",
        "role": "moving",
        "explode": [
          0.12,
          0,
          0
        ],
        "cut": false,
        "info": {
          "summary": "Swivelling clapper box and downfeed tool slide",
          "role": "Clamps the single-point cutting tool; swivels outward on the return stroke to prevent tool wear and workpiece scoring."
        },
        "motion": {
          "kind": "oscillate",
          "axis": "x",
          "speed": "speed / 60",
          "amplitude": "stroke / 2"
        },
        "mount": {
          "kind": "against",
          "target": "ram",
          "face": "+x",
          "shift": [
            0.02,
            -0.02,
            0
          ]
        },
        "shapes": [
          {
            "kind": "box",
            "position": [
              0,
              0,
              0
            ],
            "sx": 0.03,
            "sy": 0.12,
            "sz": 0.08
          },
          {
            "kind": "cylinder",
            "position": [
              0.022,
              0,
              0
            ],
            "rotation": [
              0,
              0,
              1.5708
            ],
            "r": 0.036,
            "h": 0.018
          },
          {
            "kind": "box",
            "position": [
              0.038,
              -0.02,
              0
            ],
            "sx": 0.032,
            "sy": 0.06,
            "sz": 0.05
          },
          {
            "kind": "box",
            "position": [
              0.056,
              -0.03,
              0
            ],
            "sx": 0.024,
            "sy": 0.04,
            "sz": 0.024
          },
          {
            "kind": "box",
            "position": [
              0.056,
              -0.068,
              0
            ],
            "sx": 0.014,
            "sy": 0.052,
            "sz": 0.014
          },
          {
            "kind": "cylinder",
            "position": [
              0.014,
              0.072,
              0
            ],
            "r": 0.02,
            "h": 0.012
          }
        ]
      },
      {
        "id": "work_table",
        "name": "Worktable & Machine Vise",
        "material": "castIron",
        "role": "housing",
        "explode": [
          0,
          -0.1,
          0.08
        ],
        "cut": false,
        "info": {
          "summary": "T-slotted table and knee assembly with machine vise",
          "role": "Supports and clamps the workpiece directly beneath the cutting tool path."
        },
        "mount": {
          "kind": "against",
          "target": "frame",
          "face": "+x",
          "shift": [
            0.09,
            -0.11,
            0.01
          ]
        },
        "shapes": [
          {
            "kind": "box",
            "position": [
              0,
              0,
              0
            ],
            "sx": 0.16,
            "sy": 0.2,
            "sz": 0.16
          },
          {
            "kind": "box",
            "position": [
              0.01,
              0.1,
              0
            ],
            "sx": 0.18,
            "sy": 0.035,
            "sz": 0.16
          },
          {
            "kind": "box",
            "position": [
              0.01,
              0.134,
              0
            ],
            "sx": 0.12,
            "sy": 0.034,
            "sz": 0.1
          },
          {
            "kind": "box",
            "position": [
              0.01,
              0.162,
              0
            ],
            "sx": 0.09,
            "sy": 0.024,
            "sz": 0.06
          }
        ]
      }
    ],
    "annotations": [
      {
        "id": "stroke_dim",
        "kind": "dimension",
        "label": "Stroke S",
        "magnitude": "stroke",
        "unit": "m",
        "anchor": {
          "part": "ram",
          "at": "+y"
        }
      },
      {
        "id": "cutting_force",
        "kind": "force",
        "label": "F_c",
        "magnitude": "F_cut",
        "unit": "N",
        "anchor": {
          "part": "tool_head",
          "at": "+x"
        },
        "direction": "-x",
        "length": 0.12
      },
      {
        "id": "crank_torque",
        "kind": "moment",
        "label": "T_in",
        "magnitude": "F_cut * r",
        "unit": "N·m",
        "anchor": {
          "part": "bull_gear",
          "at": "center"
        }
      }
    ],
    "calculations": [
      {
        "id": "phi_deg",
        "label": "Lever Swing Half-Angle",
        "symbol": "φ",
        "formula": "asin(r / c) * 180 / pi",
        "unit": "deg"
      },
      {
        "id": "qrr",
        "label": "Quick-Return Ratio",
        "symbol": "QRR",
        "formula": "(180 + 2 * asin(r / c) * 180 / pi) / (180 - 2 * asin(r / c) * 180 / pi)",
        "unit": ""
      },
      {
        "id": "stroke",
        "label": "Ram Stroke Length",
        "symbol": "S",
        "formula": "2 * L_lever * (r / c)",
        "unit": "m"
      },
      {
        "id": "v_cut_avg",
        "label": "Mean Cutting Speed",
        "symbol": "V_cut",
        "formula": "(2 * L_lever * (r / c)) / ((180 + 2 * asin(r / c) * 180 / pi) / 360 * (60 / speed))",
        "unit": "m/s"
      },
      {
        "id": "v_ret_avg",
        "label": "Mean Return Speed",
        "symbol": "V_ret",
        "formula": "(2 * L_lever * (r / c)) / ((180 - 2 * asin(r / c) * 180 / pi) / 360 * (60 / speed))",
        "unit": "m/s"
      },
      {
        "id": "P_cut",
        "label": "Cutting Power",
        "symbol": "P",
        "formula": "F_cut * ((2 * L_lever * (r / c)) / ((180 + 2 * asin(r / c) * 180 / pi) / 360 * (60 / speed))) / 1000",
        "unit": "kW"
      }
    ],
    "charts": [
      {
        "id": "velocity_diagram",
        "title": "Ram Linear Velocity vs Crank Angle",
        "x": {
          "label": "Crank Angle",
          "unit": "deg",
          "from": "0",
          "to": "360"
        },
        "y": {
          "label": "Ram Velocity",
          "unit": "m/s"
        },
        "series": [
          {
            "id": "v_ram",
            "label": "Velocity v(θ)",
            "formula": "2 * pi * (speed / 60) * r * (L_lever / c) * sin(x * pi / 180) / (1 - (r / c) * cos(x * pi / 180))^1.5"
          }
        ]
      },
      {
        "id": "displacement_diagram",
        "title": "Ram Position vs Crank Angle",
        "x": {
          "label": "Crank Angle",
          "unit": "deg",
          "from": "0",
          "to": "360"
        },
        "y": {
          "label": "Displacement",
          "unit": "m"
        },
        "series": [
          {
            "id": "s_ram",
            "label": "Displacement s(θ)",
            "formula": "(stroke / 2) * (1 - cos(x * pi / 180 - asin(r / c) * sin(x * pi / 180)))"
          }
        ]
      }
    ]
  },
  "view": {
    "camera": {
      "position": [
        0.55,
        0.32,
        0.62
      ],
      "target": [
        0.06,
        0.02,
        0.02
      ]
    },
    "extent": 0.6,
    "floorY": -0.26,
    "cut": {
      "enabled": false,
      "normal": [
        0,
        0,
        1
      ],
      "pos": 0
    }
  },
  "meta": {
    "generator": "Solidify (solidify.studio)",
    "license": "CC-BY-4.0",
    "created": "2026-11-10"
  }
}