A wheel clamp (200; 300; 400) for attaching to a vehicle wheel for performing a wheel alignment on the vehicle, the wheel comprising a tire and a rim, the wheel clamp (200; 300; 400) comprising: a clamp body (220; 305; 405) for supporting an apparatus used in performing the wheel alignment; three extendable arms (225; 315, 410), each slidably mounted to the clamp body (220; 305; 405) such that they extend outward radially from a central point, each extendable arm (225; 315, 410) having a gripping portion (230; 320; 415) for gripping a tread surface of the vehicle tire and a sidewall contact portion (235; 325; 420) for contacting a sidewall of the tire when the gripping portion (230; 320; 415) is gripping the tire tread surface; and a self-centering linkage mechanism (245; 330; 425) comprising a plurality of gears rotatably mounted to the clamp body (220; 305; 405) and engaged with each other, and a plurality of link arms (248; 334), each link arm (248; 334) movably connecting one of the extendable arms (225; 315; 410) to one of the gears such that when the gears are rotated, the extendable arms (225; 315; 410) simultaneously proportionally slide relative to the clamp body (220; 305; 405); wherein the linkage mechanism (245; 330; 425) is for moving the extendable arms (225; 315; 410) such that the gripping portions (230; 320; 415) of the extendable arms (225; 315; 410) engage and grip the tire tread surface and tighten the clamp (200; 300; 400) onto the tire, while the sidewall contact portions (235; 325; 420) of the extendable arms (225; 315; 410) contact the tire sidewall; and wherein the extendable arms (225; 315; 410) are for spacing the wheel clamp (200; 300; 400) away from the wheel rim when the gripping portions (230; 320; 415) are gripping the tire tread surface and the sidewall contact portions (235; 325; 420) are contacting the tire sidewall, such that the clamp body (220; 305; 405) is substantially parallel to the vehicle wheel and the wheel clamp (200; 300; 400) has no contact with the rim. a clamp body (220; 305; 405) for supporting an apparatus used in performing the wheel alignment; three extendable arms (225; 315, 410), each slidably mounted to the clamp body (220; 305; 405) such that they extend outward radially from a central point, each extendable arm (225; 315, 410) having a gripping portion (230; 320; 415) for gripping a tread surface of the vehicle tire and a sidewall contact portion (235; 325; 420) for contacting a sidewall of the tire when the gripping portion (230; 320; 415) is gripping the tire tread surface; and a self-centering linkage mechanism (245; 330; 425) comprising a plurality of gears rotatably mounted to the clamp body (220; 305; 405) and engaged with each other, and a plurality of link arms (248; 334), each link arm (248; 334) movably connecting one of the extendable arms (225; 315; 410) to one of the gears such that when the gears are rotated, the extendable arms (225; 315; 410) simultaneously proportionally slide relative to the clamp body (220; 305; 405); wherein the linkage mechanism (245; 330; 425) is for moving the extendable arms (225; 315; 410) such that the gripping portions (230; 320; 415) of the extendable arms (225; 315; 410) engage and grip the tire tread surface and tighten the clamp (200; 300; 400) onto the tire, while the sidewall contact portions (235; 325; 420) of the extendable arms (225; 315; 410) contact the tire sidewall; and wherein the extendable arms (225; 315; 410) are for spacing the wheel clamp (200; 300; 400) away from the wheel rim when the gripping portions (230; 320; 415) are gripping the tire tread surface and the sidewall contact portions (235; 325; 420) are contacting the tire sidewall, such that the clamp body (220; 305; 405) is substantially parallel to the vehicle wheel and the wheel clamp (200; 300; 400) has no contact with the rim.