{
  "commands": [
    {"command":"file.new","params":{"name":"Chebyshev lambda motion trace"}},
    {"command":"parameters.add","params":{"name":"unit_length","expression":"20 mm","favorite":true,"comment":"Chebyshev scale: crank 1, ground 2, rocker 2.5, coupler 2.5 + 2.5"}},
    {"command":"parameters.add","params":{"name":"crank_length","expression":"unit_length"}},
    {"command":"parameters.add","params":{"name":"ground_length","expression":"2 * unit_length"}},
    {"command":"parameters.add","params":{"name":"coupler_length","expression":"2.5 * unit_length","favorite":true,"comment":"Distance between the coupler pins; try 55 mm to reshape the trajectory"}},
    {"command":"parameters.add","params":{"name":"rocker_length","expression":"2.5 * unit_length"}},
    {"command":"parameters.add","params":{"name":"trace_sweep","expression":"360 deg","favorite":true,"comment":"Retained trace range; try 180 deg"}},
    {"command":"parameters.add","params":{"name":"pivot_span","expression":"sqrt(ground_length^2 + crank_length^2)"}},
    {"command":"parameters.add","params":{"name":"circle_along","expression":"(coupler_length^2 - rocker_length^2 + pivot_span^2) / (2 * pivot_span)"}},
    {"command":"parameters.add","params":{"name":"circle_height","expression":"sqrt(coupler_length^2 - circle_along^2)"}},
    {"command":"parameters.add","params":{"name":"coupler_q_x","expression":"(circle_along * ground_length + circle_height * crank_length) / pivot_span"}},
    {"command":"parameters.add","params":{"name":"coupler_q_y","expression":"crank_length + (circle_height * ground_length - circle_along * crank_length) / pivot_span"}},
    {"command":"parameters.add","params":{"name":"coupler_angle","expression":"atan2(coupler_q_y - crank_length, coupler_q_x)","unit":"deg"}},
    {"command":"parameters.add","params":{"name":"rocker_angle","expression":"atan2(coupler_q_y, coupler_q_x - ground_length)","unit":"deg"}},

    {"command":"component.create","params":{"name":"Ground"}},
    {"command":"solid.box","params":{"corner":[-7,-8,-6],"length":"ground_length + 14 mm","width":16,"height":4,"body_name":"Base"}},
    {"command":"solid.cylinder","params":{"base":[0,0,-2],"radius":4,"height":12,"body_name":"Fixed crank pivot"}},
    {"command":"solid.cylinder","params":{"base":["ground_length",0,-2],"radius":4,"height":12,"body_name":"Fixed rocker pivot"}},
    {"command":"appearance.assign","params":{"components":["Ground"],"color":"#526477"}},
    {"command":"component.activate","params":{"component":"root"}},
    {"command":"component.create","params":{"name":"Crank"}},
    {"command":"solid.box","params":{"corner":[0,-3,0],"length":"crank_length","width":6,"height":3,"body_name":"Crank bar"}},
    {"command":"solid.move","params":{"bodies":["Crank bar"],"axis":[0,0,1],"angle":"90 deg"}},
    {"command":"solid.cylinder","params":{"base":[0,0,3],"radius":3,"height":7,"body_name":"Crank bearing"}},
    {"command":"solid.cylinder","params":{"base":[0,"crank_length",3],"radius":3,"height":7,"body_name":"Crank pin"}},
    {"command":"appearance.assign","params":{"components":["Crank"],"color":"#328BD3"}},
    {"command":"component.activate","params":{"component":"root"}},
    {"command":"component.create","params":{"name":"Coupler"}},
    {"command":"solid.box","params":{"corner":[0,-2.5,3],"length":"2 * coupler_length","width":5,"height":3,"body_name":"Extended coupler"}},
    {"command":"solid.move","params":{"bodies":["Extended coupler"],"axis":[0,0,1],"angle":"coupler_angle","translate":[0,"crank_length",0]}},
    {"command":"solid.cylinder","params":{"base":[0,"crank_length",6],"radius":2.5,"height":4,"body_name":"Coupler crank pin"}},
    {"command":"solid.cylinder","params":{"base":["coupler_q_x","coupler_q_y",6],"radius":2.5,"height":4,"body_name":"Coupler rocker pin"}},
    {"command":"solid.cylinder","params":{"base":["2 * coupler_q_x","2 * coupler_q_y - crank_length",6],"radius":2,"height":4,"body_name":"Tracer tip"}},
    {"command":"appearance.assign","params":{"components":["Coupler"],"color":"#E3AB4B"}},
    {"command":"appearance.assign","params":{"bodies":["Tracer tip"],"color":"#D95360"}},
    {"command":"component.activate","params":{"component":"root"}},
    {"command":"component.create","params":{"name":"Rocker"}},
    {"command":"solid.box","params":{"corner":[0,-3,0],"length":"rocker_length","width":6,"height":3,"body_name":"Rocker bar"}},
    {"command":"solid.move","params":{"bodies":["Rocker bar"],"axis":[0,0,1],"angle":"rocker_angle","translate":["ground_length",0,0]}},
    {"command":"solid.cylinder","params":{"base":["ground_length",0,3],"radius":3,"height":7,"body_name":"Rocker bearing"}},
    {"command":"solid.cylinder","params":{"base":["coupler_q_x","coupler_q_y",3],"radius":3,"height":7,"body_name":"Rocker pin"}},
    {"command":"appearance.assign","params":{"components":["Rocker"],"color":"#3EA69B"}},
    {"command":"component.activate","params":{"component":"root"}},
    {"command":"occurrence.ground","params":{"occurrence":"Ground:1","grounded":true}},
    {"command":"joint.create","params":{"name":"Crank drive","type":"revolute","flip":true,"a":{"occurrence":"Ground","face":[0,0,10],"x":[1,0,0]},"b":{"occurrence":"Crank","face":[0,0,10],"x":[1,0,0]}}},
    {"command":"joint.create","params":{"name":"Crank to coupler","type":"revolute","flip":true,"a":{"occurrence":"Crank","face":[0,20,10],"x":[1,0,0]},"b":{"occurrence":"Coupler","face":[0,20,10],"x":[1,0,0]}}},
    {"command":"joint.create","params":{"name":"Coupler to rocker","type":"revolute","flip":true,"a":{"occurrence":"Coupler","face":[40,50,10],"x":[1,0,0]},"b":{"occurrence":"Rocker","face":[40,50,10],"x":[1,0,0]}}},
    {"command":"joint.create","params":{"name":"Rocker pivot","type":"revolute","flip":true,"a":{"occurrence":"Ground","face":[40,0,10],"x":[1,0,0]},"b":{"occurrence":"Rocker","face":[40,0,10],"x":[1,0,0]}}},
    {"command":"motion.study","params":{"name":"Chebyshev cycle","steps":72,"keys":[{"joint":"Crank drive","points":[[0,0],[72,360]]}]}},
    {"command":"motion.trace.keep","params":{"name":"Chebyshev trajectory","occurrence":"Coupler","point":[80,80,10],"point_ref":{"occurrence":"Coupler","face":[80,80,10]},"joint":"Crank drive","from":0,"to":"trace_sweep","samples":145}},
    {"command":"component.activate","params":{"component":"root"}}
  ]
}