A phacoemulsification tip, comprising - an at least partially straight shaft defining a z axis; - a cutting edge portion at a distal end of the shaft, wherein the cutting edge portion comprises at least a first and a second bend (102,104) and a distal end point; - the tip being configured to be vibrated ultrasonically torsionally when used with a phacoemulsification handpiece comprising an ultrasonic driving mechanism, whereby the ultrasonic torsional vibration of the tip results in at least two motions, comprising: - lateral displacement of the tip on an x axis perpendicular to the z axis collinear with a straight shaft portion and perpendicular to a y axis of a bend of the at least first and second bends of the tip; - twist angle along the z axis collinear with the straight shaft portion of the tip; wherein geometry of the shaft and the at least first and second bend is configured to result, during the ultrasonic torsional vibration of the tip, in a lateral displacement of the shaft, perpendicular to the shaft, of less than approximately 5 to 25% of the lateral displacement of the distal end point of the tip along a length of the shaft that extends from a proximal end of the shaft to the first bend of the cutting edge portion, wherein the lateral displacement of the tip ( u x) is at least partially determined using equation, ü x = 1 ρS z d 2 d z 2 E I y z d 2 u x d z 2 − φ d 2 l z d z 2, wherein: φ is the twist angle of the tip, ρ is density of a tip material, S ( z) is a cross-sectional area of the tip along the z axis collinear with the shaft, E is young's modulus of the tip material, I y ( z) is a moment of inertia of a cross-section of the tip around the y axis perpendicular to the axis collinear with the shaft, and l ( z) is lateral displacement along the x axis perpendicular to the z axis collinear with the shaft, wherein the at least the first and second bends (102,104) are positioned along approximately a distal 5 to 25% of a length of the tip, measured along the z axis such that the ultrasonic torsional vibration energy in the tip during the ultrasonic torsional vibration is in a twisting vibrational mode along the straight shaft portion of the tip with reduced lateral motion along the shaft with increased lateral displacement and twisting at the distal end point. - an at least partially straight shaft defining a z axis; - a cutting edge portion at a distal end of the shaft, wherein the cutting edge portion comprises at least a first and a second bend (102,104) and a distal end point; - the tip being configured to be vibrated ultrasonically torsionally when used with a phacoemulsification handpiece comprising an ultrasonic driving mechanism, - lateral displacement of the tip on an x axis perpendicular to the z axis collinear with a straight shaft portion and perpendicular to a y axis of a bend of the at least first and second bends of the tip; - twist angle along the z axis collinear with the straight shaft portion of the tip; φ is the twist angle of the tip, ρ is density of a tip material, S ( z) is a cross-sectional area of the tip along the z axis collinear with the shaft, E is young's modulus of the tip material, I y ( z) is a moment of inertia of a cross-section of the tip around the y axis perpendicular to the axis collinear with the shaft, and l ( z) is lateral displacement along the x axis perpendicular to the z axis collinear with the shaft, wherein the at least the first and second bends (102,104) are positioned along approximately a distal 5 to 25% of a length of the tip, measured along the z axis such that the ultrasonic torsional vibration energy in the tip during the ultrasonic torsional vibration is in a twisting vibrational mode along the straight shaft portion of the tip with reduced lateral motion along the shaft with increased lateral displacement and twisting at the distal end point.