Device and method for measuring rotation angle of spherical hinge joint with football-shaped structure

A method for measuring a rotation angle of a spherical hinge joint with a football-shaped structure, comprising following steps:

• Step one:
• establishing an absolute coordinate system with a spherical center position of an induction electrode system (4) as a coordinate origin;
• establishing a sub-coordinate system for each detection unit, with a coordinate origin of the sub-coordinate system in coincidence with the coordinate origin of the absolute coordinate system and a z-axis direction of the sub-coordinate system being a direction from the spherical center position of the induction electrode system (4) to a center position of a corresponding regular pentagonal spherical electrode plate (6);
• Step two:
• determining a target detection unit for measurement;
• calculating output capacitance values of all detection units, respectively;
• wherein an output capacitance value of each detection unit is a sum of the capacitance values between a regular pentagonal spherical electrode plate (6) as well as respective regular hexagonal spherical electrode plates (5) corresponding to the detection unit and the driving electrode (3), and setting a detection unit with a maximum output capacitance value as the target detection unit;
• Step three:
• acquiring a declination angle (γ, β) of the driving electrode (3) with respect to the sub-coordinate system corresponding to the target detection unit;
• 3-1:
• according to the capacitance values between the regular pentagonal spherical electrode plate (6) as well as respective regular hexagonal spherical electrode plates (5) in the target detection unit and the driving electrode (3), calculating overlapping areas S0-S5 of the driving electrode (3) with one regular pentagonal spherical electrode plate (6) and five regular hexagonal spherical electrode plates (5);
• 3-2:
• determining coordinates of a center position of the driving electrode (3) in the sub-coordinate system corresponding to the target detection unit according to the overlapping areas S0-S5;
• 3-3:
• calculating declination angles (γ, β) between the center position of the driving electrode (3) and the z axis of the sub-coordinate system according to the coordinates of the center position of the driving electrode (3) in the sub-coordinate system corresponding to the target detection unit, wherein γ is a declination angle of the center position of the driving electrode (3) around the x axis of the sub-coordinate system, and β is a declination angle of the driving electrode (3) around the y axis of the sub-coordinate system;
• and
• Step four:
• acquiring a measurement value (γsum, βsum) of the rotation angle of the spherical hinge joint, γsum=γ+γ0, βsum=β+β0, wherein γ0 is a declination angle of the sub-coordinate system corresponding to the target detection unit, with respect to the absolute coordinate system, around the x axis of the absolute coordinate system, and β0 is a declination angle of the sub-coordinate system corresponding to the target detection unit, with respect to the absolute coordinate system, around the y axis of the absolute coordinate system.