Method for determining placement of parallel-kinematic machine joints, and a parallel-kinematic machine with high stiffness

A parallel kinematic machine (PKM), comprising

• a support-platform;
• a first support linkage, comprising two or more first support-links, each of the first support-links connected at a first end to the support-platform via a first support-platform joint and at a second end connected to a first carriage via a first carriage joint, wherein the first carriage is movable along a first path, and the first support linkage is arranged to transfer a first movement to the support-platform;
• a second support linkage, comprising one or more second support-links, each of the second support-links connected at a first end to the support-platform via a second support- platform joint, and at a second end connected to a second carriage via a second carriage joint, wherein the second carriage is movable along a second path, and the second support linkage is arranged to transfer a second movement to the support-platform;
• and
• a third support linkage, comprising two or more third support-links, each of the third support-links connected at a first end to the support-platform via a third support-platform joint, and at a second end connected to a third carriage via a third carriage joint, wherein the third carriage is movable along a third path, and the third support linkage is arranged to transfer a third movement to the support-platform;
• wherein the first support linkage, the second support linkage, and the third support linkage together comprise at least five support-links;
• wherein the first movement, the second movement and the third movement position the support-platform in a base coordinate system (Xb, Yb, Zb), of which the X-axis (Xb) is parallel with the direction of at least one of the first path, the second path, and the third path, and the Z-axis (Zb) is in a direction of a normal of a plane defined by at least two of the first path, the second path, and the third path;
• wherein a first one of the first support-platform joints of the first support linkage and a first one of the third support-platform joints of the third support linkage are placed to the support-platform with a first distance (d1) between each other, and a second one of the first support-platform joints of the first support linkage and a second one of the third support-platform joints of the third support linkage are placed to the support-platform with a second distance (d2) between each other, wherein the second distance (d2) is different from the first distance (d1);
• wherein a support-platform coordinate system is defined with perpendicular axes Xsp, Ysp, Zsp with an origin at a connection point at a front face of the support-platform, wherein the Zsp-axis is in a direction of a normal of the front face;
• wherein the first one of the first support-platform joints of the first support linkage is placed to the support-platform at a fourth distance (d4) in the direction of the Zsp-axis from the connection point that is smaller than a fifth distance (d5) in the direction of the Zsp-axis from the connection point to the second one of the support-platform joints of the first support linkage, and the first one of the third support-platform joints of the third support linkage is placed to the support-platform at a sixth distance (d6) in the direction of the Zsp-axis from the connection point that is smaller than a seventh distance (d7) in the direction of the Zsp-axis from the connection point to the second one of the third support-platform joints of the third support linkage;
• and
• wherein the second one of the first support-platform joints of the first support linkage is placed to the support-platform at an eighth distance (d8) in the direction of the Xsp-axis from the first one of the first support-platform joints of the first support linkage, and the second one of the third support-platform joints of the third support linkage is placed to the support-platform at a ninth distance (d9) in the direction of the Xsp-axis from the first one of the third support-platform joints of the third support linkage.