An axial piston pump, comprising: a static head with parallel cavities in which the pistons are housed, which are configured to move axially in both directions within said cavities to supply a flow rate of fluid at the outlet of said cavities that are distributed in a circumferential path; and a regulable movement transmission system that includes at least a first rotary plate, a second rotary plate that can be tilted with respect to the first plate, and a ball joint support wherein ends of the pistons are coupled by means of end heads with double joints; - the first plate including curved-concave female front seats on which complementary curved-convex male front seats of the second tiltable plate rest; wherein the curvature of the first and the second front seats are equidistant from a shared centre located inside a main casing and - the ball joint support resting frontally on a second axial bearing coupled to an extension of the second plate; wherein said ball joint support adopts the tilt of said second plate at all times, without rotational movement of the ball joint support; wherein the regulable movement transmission system is configured to be able to vary the stroke of the pistons in order to vary the flow rate of the fluid at the outlet of the cavities; characterized in that the regulable movement transmission system further includes a third rotary plate and a mobile runner with linear movement; wherein the third plate is coupled to the mobile runner by means of an idle rotation coupling in a plane perpendicular to the linear movement of the mobile runner; wherein the first plate drags the second plate and the third plate with its rotation; and wherein the first, second and third plates, as well as the mobile runner together with a tensioning device of the transmission system are located inside the main casing; the second plate is linked to the third plate by means of a crank mechanism that hinges at a first end on the third plate by means of a first hinged connection, while a second end of the crank mechanism, opposite the first end, hinges on the second plate by means of a second hinged connection; and wherein the variation of the stroke of the pistons is carried out by means of the linear movement of the mobile runner that modifies the tilt of the second plate and of the ball joint support through the third plate and the crank mechanism. a static head with parallel cavities in which the pistons are housed, which are configured to move axially in both directions within said cavities to supply a flow rate of fluid at the outlet of said cavities that are distributed in a circumferential path; and a regulable movement transmission system that includes at least a first rotary plate, a second rotary plate that can be tilted with respect to the first plate, and a ball joint support wherein ends of the pistons are coupled by means of end heads with double joints; - the first plate including curved-concave female front seats on which complementary curved-convex male front seats of the second tiltable plate rest; wherein the curvature of the first and the second front seats are equidistant from a shared centre located inside a main casing and - the ball joint support resting frontally on a second axial bearing coupled to an extension of the second plate; wherein said ball joint support adopts the tilt of said second plate at all times, without rotational movement of the ball joint support; - the first plate including curved-concave female front seats on which complementary curved-convex male front seats of the second tiltable plate rest; wherein the curvature of the first and the second front seats are equidistant from a shared centre located inside a main casing and - the ball joint support resting frontally on a second axial bearing coupled to an extension of the second plate; wherein said ball joint support adopts the tilt of said second plate at all times, without rotational movement of the ball joint support; wherein the regulable movement transmission system is configured to be able to vary the stroke of the pistons in order to vary the flow rate of the fluid at the outlet of the cavities; characterized in that the regulable movement transmission system further includes a third rotary plate and a mobile runner with linear movement; wherein the third plate is coupled to the mobile runner by means of an idle rotation coupling in a plane perpendicular to the linear movement of the mobile runner; wherein the first plate drags the second plate and the third plate with its rotation; and wherein the first, second and third plates, as well as the mobile runner together with a tensioning device of the transmission system are located inside the main casing; the second plate is linked to the third plate by means of a crank mechanism that hinges at a first end on the third plate by means of a first hinged connection, while a second end of the crank mechanism, opposite the first end, hinges on the second plate by means of a second hinged connection; and wherein the variation of the stroke of the pistons is carried out by means of the linear movement of the mobile runner that modifies the tilt of the second plate and of the ball joint support through the third plate and the crank mechanism.